# Some properties of generalized complements of a graph

## Document Type

Article

## Publication Title

Journal of Mathematical and Computational Science

## Abstract

Let P = {V ,V , · · ·,V } be a partition of vertex set V of G. The k−complement of G denoted by G k defined as follows: for all V and V in P, i ≠ j, remove the edges between V and V and add edges between V and V which are not in G. The graph G is k-self complementary with respect to P if G k = G. The k(i)-complement G k(i)of a graph G with respect to P is defined as follows: for all Vr ∈ P, remove edges inside V and add edges which are not in V . In this paper we provide sufficient conditions for G k and G k(i) to be disconnected, regular, line preserving and Eulerian. 1 2 k i j i j i j r r P is P ∼ P P P

## First Page

2917

## Last Page

2925

## DOI

10.28919/jmcs/4982

## Publication Date

1-1-2020

## Recommended Citation

Girija, K. P.; D’souza, Sabitha; Nayak, C. Devadas; and Bhat, Pradeep G., "Some properties of generalized complements of a graph" (2020). *Open Access archive*. 346.

https://impressions.manipal.edu/open-access-archive/346