Generalized complements of a graph

Sampathkumar, E. and Latha, L. P. and Venkatachalam, C. V. and Bhat, Pradeep (1998) Generalized complements of a graph. Indian Journal of Pure & Applied Mathematics, 29 (6). pp. 625-639.

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Let G=(V,E) be a graph and P = {V-1, V-2, ..., V-k} be a partition of V of order k greater than or equal to 1. For each set V,in P, remove the edges of G inside V-r and add the edges (G) over bar, (the complement of G) joining the vertices V-r. The graph G(k)(P) (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 G(k)(P) (i) G for some partition P of V of order k. Further, G is k(i)-co-self complementary (kQ-co-s.c.) if G(k)(P) (i) congruent to (G) over bar. 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.

Item Type: Article
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: Users 23 not found.
Date Deposited: 08 Jun 2021 07:14
Last Modified: 01 Jul 2022 11:27

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