THE CONSTRUCTION OF MINIMAL‐LINE GRAPHS WITH GIVEN AUTOMORPHISM GROUP
1979; Wiley; Volume: 328; Issue: 1 Linguagem: Inglês
10.1111/j.1749-6632.1979.tb17775.x
ISSN1749-6632
AutoresDonald J. McCarthy, Louis V. Quintas,
Tópico(s)Graph theory and applications
ResumoAnnals of the New York Academy of SciencesVolume 328, Issue 1 p. 144-152 THE CONSTRUCTION OF MINIMAL-LINE GRAPHS WITH GIVEN AUTOMORPHISM GROUP Donald J. McCarthy, Donald J. McCarthy Department of Mathematics and Computer Science St. John's University Jamaica. New York 11439Search for more papers by this authorLouis V. Quintas, Louis V. Quintas Department of Mathematics Pace University New York, New York 10038 Partially supported by a Pace University Scholarly Research Committee grant.Search for more papers by this author Donald J. McCarthy, Donald J. McCarthy Department of Mathematics and Computer Science St. John's University Jamaica. New York 11439Search for more papers by this authorLouis V. Quintas, Louis V. Quintas Department of Mathematics Pace University New York, New York 10038 Partially supported by a Pace University Scholarly Research Committee grant.Search for more papers by this author First published: June 1979 https://doi.org/10.1111/j.1749-6632.1979.tb17775.xCitations: 2 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL References 1 Erdös, P. & A. Rényi. 1963. Asymmetric Graphs, Acta Math. Acad. Sci. Hung. 14: 295– 315. 2 Quintas, L. V. 1967. Extrema concerning asymmetric graphs. J. Comb. Theory 3: 57– 82. 3 Quintas, L. V. 1968. The least number of edges for graphs having symmetric automorphisrn group. J. Comb. Theory 5: 115– 125. 4 Frucht, R., A. Gewirtz & L. V. Quintas. 1970. The least number of edges for graphs having automorphism group of order three. In Recent Trends in Graph Theory. Proc. Conf., New York, 1970. Lect. Notes Math. Springer-Verlag, New York . 186: 95– 104. 5 Haggard, G. 1973. The least number of edges for graphs having dihedral automorphism group. Discrete Math. 6: 53– 78. 6 McCarthy, D. J. & L. V. Quintas. 1976. A stability theorem for minimum edge graphs with given abstract automorphism group. Trans. Am. Math. Soc. 208: 27– 39. 7 Haggard, G., D. McCarthy & A. Wohlgemuth. 1976. Extremal edge problems for graphs with given hyperoctahedral automorphism group. Discrete Math. 14: 139– 156. 8 Christopher, P. R. Minimum edge graphs with automorphism group having symmetric direct factors. Proc. 8th Southeast. Conf. Combinatorics. Graph Theory Comput, 1977. To appear. 9 Foy, G. 1975. Unicyclic graphs with a cyclic automorphism group. St. John's University. M.A. thesis. 10 McCarthy, D. 1976. Minimal edge problems for graphs with generalized symmetric automorphism group (Abstract). Not. Am. Math. Soc. 23: A512, No. 737–05–25. 11 Meriwether, R. L. 1967. Smallest graphs with a given cyclic group (Summary). In Math. Rev. 33 (2563); also, Proc. Calgary Intl. Conf, Combinatorial Struct. Appl., 1970. R. Guy et al., Eds. Gordon & Breach, New York, N.Y. pp. 103– 109. 12 Arlinghaus, W. C. Wayne State University. Doctoral dissertation (unpublished). 13 Babai, L. 1974. On the minimum order of graphs with given group. Can. Math. Bull. 17: 467– 470. 14 Harary, F. & G. Prins. 1959. The number of homeomorphically irreducible trees, and other species. Acta Math. 101: 141– 162. 15 Hell, P. 1974. Math. Rev. 48 (157). 16 Gewirtz, A. & L. V. Quintas. 1969. Connected extremal edge graphs having symmetric automorphism group. In Recent Progress in Combinatorics. W. T. Tutte, Ed. Academic Press, New York , N.Y. pp. 223– 227. 17 Gewirtz, A. & L. V. Quintas, 1971. The uniqueness of a certain graph. J. Comb. Theory. 11: 45– 53. 18 Frucht, R., A. Gewirtz & L. V. Quintas. 1973. El número mínimo de líneas para grafos conexos con grupo de automorfismos de orden 3. Scientia. 142: 72– 85. 19 MaruŠiČ, D. 1976. Minimal graphs with given cyclic automorphism group. University of Ljubljana, Yugoslavia. Publikacije El. fakulteta, Beograd, 1977. BSc. thesis. 20 Babai, L. 1973. Groups of graphs on given surfaces. Acta Math. Acad. Sci. Hung. 24: 215– 221. 21 Bouwer, I. Z. & R. Frucht. 1973. Line-minimal graphs with cyclic group. In A Survey of Combinatorial Theory. J. N. Srivastava et al., Eds. North-Holland, Amsterdam , the Netherlands . pp. 53– 67. 22 Baron, G. & W. Imrich, 1969. Asymmetrische reguláre graphen. Acta Math. Acad. Sci. Hung. 20: 135– 142. 23 Gewirtz, A., A. Hill & L. V. Quintas. 1969. El número mínimo de puntos para grafos regulares y asimétricos. Scientia. 138: 103– 111. 24 Bouwer, I. Z. 1969. Section graphs for finite permutation groups. In The Many Facets of Graph Theory. Proc. Conf. Kalamazoo, Mich., 1968. Lect. Notes Math. Springer-Verlag, New York , N.Y. 110: 55– 61. 25 Nowrrz, L. A. & M. E. Watkins. 1972. Graphical regular representations of non-abelian groups I, II. Can. J. Math. 24: 993– 1008, 109–1018. 26 Imrich, W. & M. E. Watkins. 1974. On graphical regular representations of cyclic extensions of groups. Pac. J. Math. 55: 461– 477. 27 McCarthy, D. J. 1979. Extremal problems for graphs with dihedral automorphism group. Proc. Second Int. Conf. Combinatorial Math., 1978. Ann. N.Y. Acad. Sci. Citing Literature Volume328, Issue1Topics in Graph TheoryJune 1979Pages 144-152 ReferencesRelatedInformation
Referência(s)