On The k-LCM Cordial Labelling

Abstract

This paper introduces the concept of -LCM cordial labelling, a graph labelling method evolving from cordial labelling, for connected and undirected simple . Utilizing a function , where  and , each edge is assigned a label , when  and  are adjacent vertices. A -LCM Cordial Labelling is defined by two conditions:  maintaining an absolute difference of at most one in the count of vertices labelled with any  and ,and  likewise, providing an absolute difference of at most one in the count of edges labelled with  and ,for all  A graph is said to be  LCM cordial graph if such a function exists. In our investigation of -LCM cordiality, we delve into various types and specific examples of graphs. Notably, we found that cyclic graphs  do not exhibit -LCM cordiality, whereas star graphs  do. Furthermore, we examine the -LCM cordiality of lantern star graphs and  connected copies of star graphs. Moreover, we investigated the influence of pendant vertices on -LCM cordiality.