Harmonic Mean Cordial Labeling of Some Familes of Triangular Snake and Quadrilateral Snake Graphs

Abstract

A function  on a graph , where  is a simple, connected, finite and an undirected graph, is called Harmonic Mean Cordial if the induced function  defined by  satisfies the condition  and  for any , where  denote the number of vertices labelled as  and  denote the number of edges labelled as  respectively. A graph  that permits Harmonic Mean Cordial labeling is called a Harmonic Mean Cordial graph. The concepts that have have been obtained for the snake graph families have been used in applications of civil engineering, compture science, network optimization, coding theory, biology, etc. The current study has validated some theorems regarding Harmonic Mean Cordial labeling of several types of snake graphs and families of snake graphs such as double triangular snake graph, alternate triangular and quadrilateral snake graphs, double alternate triangular and quadrilateral snake graphs, spiked snake graph and alternate zig-zag triangular snake graph. The authors have also shown in past works the effectiveness of Harmonic Mean Cordial labeling in civil engineering applications in building bridges.