Generalized complements of a graph

E. Sampathkumar, L. Pushpa Latha, C. V. Venkatachalam, Pradeep Bhat

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let G = (V, E) be a graph and P = {V1, V2, ..., Vk} be a partition of V of order k ≥ 1. For each set Vr in P, remove the edges of G inside Vr and add the edges Ḡ, (the complement of G) joining the vertices Vr. The graph GPk (i) thus obtained is called the k(i)-complement of G with respect to P. The graph G is k(i)-self complementary (k(i)-s.c) if GPk (i) ≅ G for some partition P of V of order k. Further, G is k(i)co-self complementary (k(i)-co-s.c.) if GPk(i) ≅ Ḡ. We determine (1) all k(i)-s.c trees for k = 2, 3, and (2) 2(i)-s.c. unicyclic graphs. Also, some necessary conditions for a tree/unicyclic graph to be k(i)-s.c. are obtained. We indicate how to obtain characterizations of all k(i)-co.s.c. trees, unicyclic graphs and forests from known results.

Original languageEnglish
Pages (from-to)625-639
Number of pages15
JournalIndian Journal of Pure and Applied Mathematics
Volume29
Issue number6
Publication statusPublished - 01-06-1998

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Unicyclic Graph
Joining
Complement
Graph in graph theory
Partition
Necessary Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Sampathkumar, E., Pushpa Latha, L., Venkatachalam, C. V., & Bhat, P. (1998). Generalized complements of a graph. Indian Journal of Pure and Applied Mathematics, 29(6), 625-639.
Sampathkumar, E. ; Pushpa Latha, L. ; Venkatachalam, C. V. ; Bhat, Pradeep. / Generalized complements of a graph. In: Indian Journal of Pure and Applied Mathematics. 1998 ; Vol. 29, No. 6. pp. 625-639.
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Sampathkumar, E, Pushpa Latha, L, Venkatachalam, CV & Bhat, P 1998, 'Generalized complements of a graph', Indian Journal of Pure and Applied Mathematics, vol. 29, no. 6, pp. 625-639.

Generalized complements of a graph. / Sampathkumar, E.; Pushpa Latha, L.; Venkatachalam, C. V.; Bhat, Pradeep.

In: Indian Journal of Pure and Applied Mathematics, Vol. 29, No. 6, 01.06.1998, p. 625-639.

Research output: Contribution to journalArticle

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Sampathkumar E, Pushpa Latha L, Venkatachalam CV, Bhat P. Generalized complements of a graph. Indian Journal of Pure and Applied Mathematics. 1998 Jun 1;29(6):625-639.