Edward J. Farrell
Born:
place:
B.Sc. UWI, M.Math,
Ph.D. 1973 Waterloo University (Canada)
thesis: On a general class of graph polynomials; advisor Ronald C. Read
Professor of Mathematics, University of West Indies, St. Augustine, Trinidad - Trinidad and Tobago
personal or universal URL:
email: farrell@centre.uwi.ttRESEARCH
. Beezer, Robert A.; Farrell, E. J. The matching polynomial of a distance-regular graph. Int. J. Math. Math. Sci. 23 (2000), no. 2, 89--97.
. Farrell, E. J. Matchings in pentagonal cacti. J. Math. Sci. (Calcutta) 11 (2000), no. 2, 109--126.
. Farrell, E. J.; de Matas, C. M. Star polynomials of some families of graphs with small cyclomatic numbers. Util. Math. 58 (2000), 87--96.
. Farrell, E. J. Matchings in triangular cacti. J. Math. Sci. (Calcutta) 11 (2000), no. 1, 85--98.
. Farrell, E. J. Decomposition of complete graphs and complete bipartite graphs into complete bipartite factors. J. Math. Sci. (Calcutta) 11 (2000), no. 1, 29--33.
. Farrell, Edward J.; Rosenfeld, Vladimir R. Block and articulation node polynomials of the generalized rooted product of graphs. J. Math. Sci. (Calcutta) 11 (2000), no. 1, 35--47.
. Farrell, E. J.; Wahid, S. A. $D$-graphs. IV. Constructions of $D$-graphs for linear cacti. Bull. Inst. Combin. Appl. 30 (2000), 25--42.
. Farrell, E. J. On the derivative of the chromatic polynomial. Bull. Inst. Combin. Appl. 29 (2000), 33--38.
. Farrell, Edward J.; Kennedy, John W.; Quintas, Louis V. Permanents and determinants of graphs: a cycle polynomial approach. J. Combin. Math. Combin. Comput. 32 (2000), 129--137.
. Farrell, E. J.; de Matas, C. M. Algorithms for star polynomials of graphs. J. Math. Sci. (Calcutta) 10 (1999), no. 2, 69--76.
. Farrell, Edward J.; Kennedy, John W.; Quintas, Louis V. Permanents of matrices: a graph cycle polynomial approach. Bull. Inst. Combin. Appl. 28 (2000), 99--106.
. Farrell, E. J.; Wahid, S. A. $D$-graphs. II. Constructions of $D$-graphs for some families of graphs with even cycles. Util. Math. 56 (1999), 167--176.
. Farrell, Edward J.; Kennedy, John W.; Quintas, Louis V. Permanents, determinants, and cycle polynomials. New York Graph Theory Day, 36 (Staten Island, NY, 1998). Graph Theory Notes N. Y. 36 (1999), 30--34.
. Farrell, Edward J. An introduction to clique polynomials. New York Graph Theory Day, 35 (1998). Graph Theory Notes N. Y. 35 (1998), 13--15.
. Farrell, E. J. Matchings in rectangular cacti. J. Math. Sci. (Calcutta) 9 (1998), no. 2, 163--183.
. Farrell, E. J. A note on the clique polynomial and its relation to other graph polynomials. J. Math. Sci. (Calcutta) 8 (1997), no. 2, 97--102.
. Farrell, Edward J. On circuit polynomials and determinants of matrices. Dedicated to the memory of Paul Erdös (Riverdale, NY, 1996). Graph Theory Notes N. Y. 32 (1997), 47--52.
. Farrell, E. J.; Ramsamooj, N. On the derivatives of a certain characteristic polynomial. J. Math. Sci. (Calcutta) 9 (1998), no. 1, 93--99.
. Farrell, Edward J. The impact of $F$-polynomials in graph theory. Quo vadis, graph theory?, 173--178, Ann. Discrete Math., 55, North-Holland, Amsterdam, 1993.
. Beezer, Robert A.; Farrell, E. J. Counting subgraphs of a regular graph. J. Math. Sci. (Calcutta) 9 (1998), no. 1, 47--55.
. Farrell, E. J. Three-discordant permutations revisited. J. Math. Sci. (Calcutta) 9 (1998), no. 1, 9--20. [18] 99d:05061 Farrell, Edward J.; Kennedy, John W.; Quintas, Louis V. Graph permanent, determinant and cycle polynomials. Bull. Inst. Combin. Appl. 23 (1998), 73--82. [19] 98m:05144 Farrell, E. J. Matching in cacti. J. Math. Sci. (Calcutta) 8 (1997), no. 2, 85--96. [20] 98i:05117 Farrell, E. J.; Grell, J. C. On circuit polynomials and determinants of matrices. J. Combin. Math. Combin. Comput. 26 (1998), 139--146. [21] 98c:05118 Farrell, E. J.; Constantine, G. M. On the reconstruction of the subgraph polynomial and the reconstruction conjecture. J. Math. Sci. (Calcutta) 5 (1994), no. 1, 1--9. [22] 98b:05077 Farrell, E. J.; Guo, J. M. On the matching polynomials of graphs with cutsets, and applications. J. Math. Sci. (Calcutta) 5 (1994), no. 2, 33--44. [23] 97m:05221 Farrell, E. J.; Guo, J. M. On the characterizing properties of the circuit polynomial. J. Combin. Math. Combin. Comput. 24 (1997), 193--200. [24] 97g:05131 Beezer, R. A.; Riegsecker, J.; Smith, B.; Farrell, E. J. Graphs with a minimum number of pairs of independent edges. I. Matching polynomials. Bull. Inst. Combin. Appl. 18 (1996), 17--32. [25] 97d:05198 Farrell, E. J.; Guo, J. M.; Guo, Z. Y. On the strong circuit uniqueness and its application to the circuit characterization of graphs. J. Combin. Math. Combin. Comput. 20 (1996), 139--154. [26] 96m:05136 Farrell, E. J.; Wahid, S. A. $D$-graphs. I. An introduction to graphs whose matching polynomials are determinants of matrices. Bull. Inst. Combin. Appl. 15 (1995), 81--86. [27] 96a:05122 Farrell, E. J.; Chee, M. A. Sam Clique decompositions of strong short ladders. J. Combin. Math. Combin. Comput. 18 (1995), 151--160. [28] 96a:05112 Beezer, Robert A.; Farrell, E. J. The matching polynomial of a regular graph. Discrete Math. 137 (1995), no. 1-3, 7--18. [29] 94m:05139 Farrell, E. J.; Wahid, S. A. On the pseudo-matching polynomial of a graph. Vishwa Internat. J. Graph Theory 1 (1992), no. 2, 141--148. [30] 94c:05057 Farrell, E. J. A graph-theoretic approach to rook theory. Caribbean J. Math. 7 (1988), no. 1-2, 47 pp. [31] 94a:05151 Farrell, E. J. On $F$-polynomials and reconstruction. Advances in graph theory, 155--162, Vishwa, Gulbarga, 1991. [32] 93m:05150 Farrell, Edward J.; Kennedy, John W.; Quintas, Louis V.; Wahid, Shanaz A. Graphs with palindromic matching and characteristic polynomials. Vishwa Internat. J. Graph Theory 1 (1992), no. 1, 59--76. [33] 93h:05125 Farrell, E. J.; Whitehead, Earl Glen, Jr. Connections between the matching and chromatic polynomials. Internat. J. Math. Math. Sci. 15 (1992), no. 4, 757--766. [34] 93f:05070 Farrell, E. J.; Grell, J. On cocircuit graphs. J. Combin. Math. Combin. Comput. 12 (1992), 7--15. [35] 93b:05132 Farrell, E. J. On the theory of matching equivalent graphs and rook equivalent chessboards. J. Franklin Inst. 329 (1992), no. 1, 45--64. [36] 92m:05156 Farrell, E. J. An introduction to $F$-graphs, a graph-theoretic representation of natural numbers. Internat. J. Math. Math. Sci. 15 (1992), no. 2, 313--317. [37] 92d:05124 Farrell, E. J.; Guo, J. M.; Constantine, G. M. On matching coefficients. Discrete Math. 89 (1991), no. 2, 203--210. [38] 92b:05037 Farrell, E. J.; Whitehead, Earl Glen, Jr. Matching, rook and chromatic polynomials and chromatically vector equivalent graphs. J. Combin. Math. Combin. Comput. 9 (1991), 107--118. [39] 91j:05087 Farrell, E. J.; Wahid, S. A. A note on the characterization of thistles by their matching polynomials. J. Combin. Math. Combin. Comput. 8 (1990), 97--101 [40] 91j:05080 Farrell, E. J.; Whitehead, Earl Glen, Jr. On matching and chromatic properties of circulants. J. Combin. Math. Combin. Comput. 8 (1990), 79--88. [41] 91i:05097 Farrell, E. J.; Guo, J. M. On circuit characterizations of nearly regular graphs. Match No. 25 (1990), 115--130. [42] 91i:05096 Farrell, E. J. The lost species of triangular animals. Caribbean J. Math. 6 (1987), no. 1-2, 31--34. [43] 91h:05092 Farrell, E. J. Decompositions of some classes of trees into node disjoint paths. Caribbean J. Math. 6 (1987), no. 1-2, 35--45. [44] 91b:05143 Farrell, E. J.; De Matas, C. M. On star polynomials of complements of graphs. Ark. Mat. 26 (1988), no. 2, 185--190. [45] 90m:05097 Farrell, F. J. A survey of the characterizing properties of $F$-polynomials. Recent studies in graph theory, 106--113, Vishwa, Gulbarga, 1989. [46] 89k:05082 Farrell, E. J. On a class of polynomials associated with the cliques in a graph and its applications. Internat. J. Math. Math. Sci. 12 (1989), no. 1, 77--84. [47] 89e:05156 Farrell, E. J. On the matching polynomial and its relation to the rook polynomial. J. Franklin Inst. 325 (1988), no. 4, 527--543. [48] 89e:05155 Farrell, E. J. Matchings in square animals. J. Combin. Inform. System Sci. 9 (1984), no. 4, 197--206. [49] 89b:05140 Farrell, E. J.; De Matas, C. M. On the characterizing properties of star polynomials. Utilitas Math. 33 (1988), 33--45. [51] 89a:92082 Farrell, E. J.; Grell, J. C. Cycle decompositions of linear benzene chains. Match No. 21 (1986), 325--337. [52] 88m:05058 Farrell, E. J.; De Matas, C. M. On star polynomials, graphical partitions and reconstruction. Internat. J. Math. Math. Sci. 11 (1988), no. 1, 87--93. [53] 88k:05155 Farrell, E. J. On $F$-polynomials of thistles. J. Franklin Inst. 324 (1987), no. 3, 341--349. [54] 88j:05035 Farrell, E. J. Counting matchings in graphs. J. Franklin Inst. 324 (1987), no. 3, 331--339. [55] 88j:05034 Farrell, E. J.; Guo, J. M. Circuit characterizations of unions of graphs. J. Combin. Math. Combin. Comput. 2 (1987), 161--177 [56] 88e:05089 Farrell, E. J.; Wahid, S. A. Some general classes of comatching graphs. Internat. J. Math. Math. Sci. 10 (1987), no. 3, 519--524. [57] 88b:05103 Farrell, E. J. Matchings in hexagonal cacti. Internat. J. Math. Math. Sci. 10 (1987), no. 2, 321--338. [58] 87m:05134 Farrell, E. J.; Grell, J. C. An application of circuit polynomials to the counting of spanning trees in graphs. Publ. Inst. Math. (Beograd) (N.S.) 39(53) (1986), 63--67. [59] 87m:05129 Farrell, E. J.; Wahid, S. A. On the reconstruction of the matching polynomial and the reconstruction conjecture. Internat. J. Math. Math. Sci. 10 (1987), no. 1, 155--162. [60] 87i:92069b Graovac, Ante; Babi\'c, Darko Comment on: "Matchings in long benzene chains" [Match No. 18 (1985), 37--48; MR 87i:92069a] by E. J. Farrell and S. A. Wahid. Match No. 18 (1985), 49--53. [61] 87i:92069a Farrell, E. J.; Wahid, S. A. Matchings in long benzene chains. Match No. 18 (1985), 37--48. [62] 87i:05154 Farrell, E. J.; Wahid, S. A. Matching polynomials: a matrix approach and its applications. J. Franklin Inst. 322 (1986), no. 1, 13--21. [63] 87i:05153 Farrell, E. J.; Grell, J. C. Some further constructions of cocircuit and cospectral graphs. Caribbean J. Math. 4 (1985), no. 1, 17--28. [64] 87g:05176 Farrell, E. J. On the occurrences of Fibonacci sequences in the counting of matchings in linear polygonal chains. Fibonacci Quart. 24 (1986), no. 3, 238--246. [65] 87f:05128 Farrell, E. J.; Wahid, S. A. Matchings in nonagonal and decagonal chains. Caribbean J. Math. 3 (1984), no. 2, 73--84. [66] 87e:05093 Farrell, E. J.; Gutman, I. A note on the circuit polynomial and its relation to the $µ$-polynomial. Match No. 18 (1985), 55--61 [67] 87d:05128 Farrell, E. J.; Grell, J. C. Circuit polynomials, characteristic polynomials and $µ$-polynomials of some polygonal chains. Match No. 18 (1985), 17--35. [68] 87d:05127 Farrell, E. J. Decompositions of graphs with cyclomatic number $2$ into node disjoint paths. Indian J. Math. 26 (1984), no. 1-3, 1--13 (1985). [69] 87c:05091 Farrell, E. J.; Wahid, S. A. Matchings in heptagonal and octagonal chains. Caribbean J. Math. 3 (1984), no. 2, 45--57. [70] 87b:05105 Farrell, E. J. On coefficients of circuit polynomials and characteristic polynomials. Internat. J. Math. Math. Sci. 8 (1985), no. 4, 697--705. [71] 86m:05055 Farrell, E. J. A note on cycle decompositions of complete bipartite graphs. Caribbean J. Math. 3 (1984), no. 1, 9--15. [72] 86h:92061 Gutman, I.; Farrell, E. J.; Wahid, S. A. On the matching polynomials of graphs containing benzenoid chains. J. Combin. Inform. System Sci. 8 (1983), no. 2, 159--168. [73] 86d:05095 Farrell, E. J. On the number of $2$-factors in the short ladder. J. Combin. Inform. System Sci. 8 (1983), no. 3, 175--180. [74] 86a:05097 Farrell, E. J.; Grell, J. C. Some analytical properties of the circuit polynomial of a graph. Caribbean J. Math. 2 (1983), no. 3, 69--76. [75] 86a:05096 Farrell, E. J. The subgraph polynomial and its relation to some other graph polynomials. Caribbean J. Math. 2 (1983), no. 3, 39--53. [76] 85k:05074 Farrell, E. J.; Grell, J. C. The circuit polynomial and its relation to other graph polynomials. Caribbean J. Math. 2 (1983), no. 1-2, 15--24. [77] 85j:05034 Farrell, E. J. A survey of the unifying effects of $F$-polynomials in combinatorics and graph theory. Graph theory (Novi Sad, 1983), 137--150, Univ. Novi Sad, Novi Sad, 1984. [78] 85h:05082 Farrell, E. J.; Wahid, S. A. Matchings in pentagonal chains. Discrete Appl. Math. 8 (1984), no. 1, 31--40. [79] 85h:05061 Farrell, E. J. On coefficients of path polynomials. Internat. J. Math. Math. Sci. 7 (1984), no. 1, 65--73. [80] 85d:05190 Farrell, E. J. Decomposition of complete graphs and complete [bipartite] graphs into node disjoint paths. Pure Appl. Math. Sci. 17 (1983), no. 1-2, 7--14. [81] 85d:05181 Farrell, E. J.; Grell, J. C. On reconstructing the circuit polynomial of a graph. Caribbean J. Math. 1 (1982), no. 3, 109--119. [82] 85c:05023 Farrell, E. J. Forest decompositions of graphs with cyclomatic number $3$. Internat. J. Math. Math. Sci. 6 (1983), no. 3, 535--543. [83] 85c:05022 Farrell, E. J. Path decompositions of chains and circuits. Internat. J. Math. Math. Sci. 6 (1983), no. 3, 521--533. [84] 85a:05067 Farrell, E. J.; Wahid, S. A. Matchings in benzene chains. Discrete Appl. Math. 7 (1984), no. 1, 45--54. [85] 85a:05066 Farrell, E. J. On a class of polynomials associated with the paths in a graph and its application to minimum nodes disjoint path coverings of graphs. Internat. J. Math. Math. Sci. 6 (1983), no. 4, 715--726. [86] 84h:05100 Farrell, E. J. Forest decompositions of ladders. Discrete Math. 44 (1983), no. 3, 267--274. [87] 84c:05069 Farrell, E. J. Matchings in triangular animals. J. Combin. Inform. System Sci. 7 (1982), no. 2, 143--154. [88] 84b:05082 Farrell, E. J. On a class of polynomials associated with the subgraphs of a graph and its application to chromatic and dichromatic polynomials. Bull. Austral. Math. Soc. 26 (1982), no. 3, 343--354. [89] 84b:05040 Farrell, E. J. Forest decompositions of graphs with cyclomatic number $2$. Internat. J. Math. Math. Sci. 6 (1983), no. 1, 125--136. [90] 83m:05107 Farrell, E. J. A note on the circuit polynomials and characteristic polynomials of wheels and ladders. Discrete Math. 39 (1982), no. 1, 31--36. [91] 83k:05089 Farrell, E. J. Cycle decompositions of complete graphs. Discrete Math. 38 (1982), no. 2-3, 157--162. [92] 83g:05033 Farrell, E. J. A generalization of the dichromatic polynomial of a graph. Internat. J. Math. Math. Sci. 4 (1981), no. 4, 725--729. [93] 83e:05096 Farrell, E. J. On coefficients of star polynomials. Proceedings of the Third Caribbean Conference on Combinatorics and Computing (Bridgetown, 1981), pp. 110--124, Univ. West Indies, Cave Hill Campus, Barbados, 1981. [94] 83d:05035 Farrell, E. J. Forest decompositions of wheels and fans. Ars Combin. 11 (1981), 251--263. [95] 82m:05037 Farrell, E. J. Tree polynomials of complete graphs and complete bipartite graphs. Pure Appl. Math. Sci. 13 (1981), no. 1-2, 7--13. [96] 82d:05059 Farrell, E. J. A result on co-chromatic graphs. Internat. J. Math. Math. Sci. 4 (1981), no. 2, 365--369. [97] 82b:05102 Farrell, E. J. Defect-$d$ matchings in graphs with cyclomatic numbers $0$, $1$ and $2$. Discrete Math. 33 (1981), no. 3, 259--266. [98] 81j:05095 Farrell, E. J. The matching polynomial and its relation to the acyclic polynomial of a graph. Ars Combin. 9 (1980), 221--228. [99] 81j:05069 Farrell, E. J. Spanning trees in graphs with cyclomatic numbers $2$, $3$, and $4$. J. Combin. Inform. System Sci. 5 (1980), no. 1, 38--46. [100] 81i:05105 Farrell, E. J. Matchings in complete graphs and complete bipartite graphs. J. Combin. Inform. System Sci. 5 (1980), no. 1, 47--51. [101] 81i:05055 Farrell, E. J. The tree polynomial of a graph. J. Combin. Inform. System Sci. 4 (1979), no. 3, 211--218.
. Farrell, E. J. Chromatic roots---some observations and conjectures. Discrete Math. 29 (1980), no. 2, 161--167.
8. Farrell, E. J. On chromatic coefficients. Discrete Math. 29 (1980), no. 3, 257--264. [103] 81c:05073 Farrell, E. J. Matchings in wheels. Ars Combin. 8 (1979), 109--115.
7. Farrell, E. J. An introduction to matching polynomials. J. Combin. Theory Ser. B 27 (1979), no. 1, 75--86.
6. Farrell, E. J. On a general class of graph polynomials. J. Combin. Theory Ser. B 26 (1979), no. 1, 111--122.
5. Farrell, E. J. On a class of polynomials associated with the stars of a graph and its application to node-disjoint decompositions of complete graphs and complete bipartite graph. Canad. Math. Bull. 22 (1979), no. 1, 35--46.
4. Farrell, E. J. On a class of polynomials obtained from the circuits in a graph and its application to characteristic polynomials of graphs. Discrete Math. 25 (1979), no. 2, 121--133.
3. Farrell, E. J. Matchings in ladders. Ars Combin. 6 (1978), 153--161.
2. Farrell, E. J. On graphical partitions and planarity. Discrete Math. 18 (1977), no. 2, 149--153.
1. Farrell, Edward J. Uniqueness of the electromagnetic field in the Rainich unified field theory. Tensor (N.S.) 12 1962 263--277.
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