On Recent Advances in Divisor Cordial Labeling of Graphs
Vishally Sharma, Angamuthu Parthiban · Mathematics and Statistics · 2022
An assignment of intergers to the vertices of a graph subject to certain constraints is called a vertex labeling of . Different types of graph labeling techniques are used in the field of coding theory, cryptography, radar, missile guidance, -ray crystallography etc. A DCL of is a bijective function from node set of to such that for each edge , we allot 1 if divides or divides & 0 otherwise, then the absolute difference between the number of edges having 1 & the number of edges having 0 do not exceed 1, i.e., . If permits a DCL, then it is called a DCG. A complete graph , is a graph on nodes in which any 2 nodes are adjacent and lilly graph is formed by joining , sharing a common node. i.e., , where is a complete bipartite graph & is a path on nodes. In this paper, we propose an interesting conjecture concerning DCL for a given , besides, discussing certain general results concerning DCL of complete graph -related graphs. We also prove that admits a DCL for all . Further, we establish the DCL of some -related graphs in the context of some graph operations such as duplication of a node by an edge, node by a node, extension of a node by a node, switching of a node, degree splitting graph, & barycentric subdivision of the given .