Several Results on Sum Divisor Cordial Graph

Abstract

A sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, · · · , |V (G)|} such that an edge uv is assigned the label 1 if 2 divides f(u) + f(v) and 0 otherwise; and the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that every transformed tree admits sum divisor cordial labeling. Also, we investigate the sum divisor cordial labeling of the graph obtained by identifying the vertex of graphs. Finally, we discuss the sum divisor cordial labeling of splitting graph and middle graph.

Key words and phrases. Sum divisor cordial labeling, transformed tree, splitting graph.

2000 Mathematics Subject Classification. 05C78