Some properties of generalized complements of a graph

K. P. Girija, Sabitha D’souza, C. Devadas Nayak, Pradeep G. Bhat

Research output: Contribution to journalArticlepeer-review

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 GPk = 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.

Original languageEnglish
Pages (from-to)2917-2925
Number of pages9
JournalJournal of Mathematical and Computational Science
Volume10
Issue number6
DOIs
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computational Theory and Mathematics

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