Perfect 2-Colorings of k-Regular Graphs

Farzaneh Piri*; Saeed Mohammadian Semnani

doi:10.5666/KMJ.2020.60.2.349

Article

Kyungpook Mathematical Journal 2020; 60(2): 349-359

Published online June 30, 2020

Perfect 2-Colorings of k-Regular Graphs

Farzaneh Piri*, Saeed Mohammadian Semnani

Department of Applied Mathematics, Faculty of Mathematics, Statistics and Com- puter Science, University of Semnan, Semnan, Iran
e-mail : f.piri@semnan.ac.ir and s_mohammadian@semnan.ac.ir

Received: May 7, 2017; Revised: August 31, 2019; Accepted: October 4, 2019

Abstract

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Abstract

We study perfect 2-colorings of regular graphs. In particular, we consider the 4-regular case. We obtain a characterization of perfect 2-colorings of toroidal grids.

Keywords: perfect 2-coloring, regular graph, toroidal grid graph