Mean Cordial Labeling of Some Families of Ladder Graph

Abstract

Consider a function  that maps the vertex set  of a graph  to the set . Each edge  is then assigned a numerical label from based on . The labeling  is defined as a mean cordial labeling if it satisfies the following conditions:

1. For any , the absolute difference between the counts of vertices labeled  and, denoted , is at most 1.
2. Similarly, the absolute difference between the counts of edges labeled  and , denoted , is also at most 1.

Here,  and  represent the number of vertices and edges, respectively, labeled  for . A graph  that admits such a labeling is referred to as a mean cordial graph.

This chapter explores the mean cordial labeling patterns of two specific graph families: the triangular ladder  and the slanting ladder .