# Complement of a graph: A generalization

Sampathkumar, E. and Pushpalatha, L. (1998) Complement of a graph: A generalization. Graphs and Combinatorics, 14 (4). pp. 377-392.

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## Abstract

Let G = (V, E) be a graph and P = (V-1, V-2,..., V-k} be a partition of V. The k-complement G(k)(P) (With respect to P) is defined as follows: For all V-i and V-j in P, i not equal j, remove the edges between V-i and V-j, and add the edges which are not in G. A graph G is k-self complementary, if there exists a partition P of order k such that G(k)(p) congruent to G. For 2 less than or equal to k less than or equal to p, characterizations of all k-self complementary trees, forests and connected unicyclic graphs of order p are obtained.

Item Type: Article E Mathematical Science > Mathematics Department of > Mathematics Users 23 not found. 05 Jun 2021 07:36 05 Jun 2021 07:36 http://eprints.uni-mysore.ac.in/id/eprint/16737