Some Edge Product Cordial Graphs in the Context of Duplication of Some Graph Elements  

作　　者：Udayan M. Prajapati Prakruti D. Shah Udayan M. Prajapati;Prakruti D. Shah(St. Xavier’s College, Ahmedabad, India;Shankersinh Vaghela Bapu Institute of Technology, Gandhinagar, India)

机构地区：[1]St. Xavier’s College, Ahmedabad, India [2]Shankersinh Vaghela Bapu Institute of Technology, Gandhinagar, India

出　　处：《Open Journal of Discrete Mathematics》2016年第4期248-258,共11页离散数学期刊（英文）

摘　　要：For a graph, a function is called an edge product cordial labeling of G, if the induced vertex labeling function is defined by the product of the labels of the incident edges as such that the number of edges with label 1 and the number of edges with label 0 differ by at most 1 and the number of vertices with label 1 and the number of vertices with label 0 differ by at most 1. In this paper, we show that the graphs obtained by duplication of a vertex, duplication of a vertex by an edge or duplication of an edge by a vertex in a crown graph are edge product cordial. Moreover, we show that the graph obtained by duplication of each of the vertices of degree three by an edge in a gear graph is edge product cordial. We also show that the graph obtained by duplication of each of the pendent vertices by a new vertex in a helm graph is edge product cordial.For a graph, a function is called an edge product cordial labeling of G, if the induced vertex labeling function is defined by the product of the labels of the incident edges as such that the number of edges with label 1 and the number of edges with label 0 differ by at most 1 and the number of vertices with label 1 and the number of vertices with label 0 differ by at most 1. In this paper, we show that the graphs obtained by duplication of a vertex, duplication of a vertex by an edge or duplication of an edge by a vertex in a crown graph are edge product cordial. Moreover, we show that the graph obtained by duplication of each of the vertices of degree three by an edge in a gear graph is edge product cordial. We also show that the graph obtained by duplication of each of the pendent vertices by a new vertex in a helm graph is edge product cordial.

关 键 词：Graph Labeling Edge Product Cordial Labeling Duplication of a Vertex 

分 类 号：O15[理学—数学]