Some properties of generalized complements of a graph

Document Type

Article

Publication Title

Journal of Mathematical and Computational Science

Abstract

Let P = {V1,V2, · · ·,Vk } be a partition of vertex set V of G. The k−complement of G denoted by GPkis defined as follows: for all Vi and Vj in P, i ≠ j, remove the edges between Vi and Vj and add edges between Vi and Vj which are not in G. The graph G is k-self complementary with respect to P if GP∼k = G. The k(i)-complement GPk(i)of a graph G with respect to P is defined as follows: for all Vr ∈ P, remove edges inside Vr and add edges which are not in Vr. In this paper we provide sufficient conditions for GPk and GPk(i) to be disconnected, regular, line preserving and Eulerian.

First Page

2917

Last Page

2925

DOI

10.28919/jmcs/4982

Publication Date

1-1-2020

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