A study on roman domination lower deg-centric graphs

Timmy Tomy Thalavayalil1
1Department of Mathematics, Kristu Jayanti (Deemed to be University), Bengaluru-560077, India

Abstract

The lower deg-centric graph of a simple, connected graph \(G\), denoted by \(G_{ld}\), is a graph constructed from \(G\) such that \(V(G_{ld}) = V(G)\) and \(E(G_{ld}) = \{v_iv_j: d_G(v_i,v_j) < \deg_G(v_i)\}\). This paper presents the Roman domination number of lower deg-centric graphs. Also, investigate the properties and structural characteristics of this type of graph.

Keywords: distance, deg-centric graph, lower deg-centric graph, domination, Roman domination