Special Class of Mean Square Cordial Graphs

Abstract

Let G = (V,E) be a graph with p vertices and q edges. A Mean Square Cordial Labeling of a Graph G with vertex set V is a bijection from V to {0, 1} such that each edge uv is assigned the label �ሺ�ڿሺሺݑሻሻ ଶ ൅ሺ ሺݑሻሻ ଶ ۀ�ሻ 2 ⁄ where ڿ xۀ (ceilex) is the least integer greater than or equal to x with the condition that the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. The graph that admits a Mean Square Cordial Labeling is called Mean Square Cordial Graph. In this paper, we proved that the graphs Tree Tr(n), Umbrella U(n,3), Twig Tgn are Mean Square Cordial Graphs.