Cordial Labeling of Goldberg Snark and its related Graphs

TL;DR

This paper explores the application of Cordial labeling to Goldberg Snark graphs, a specific class of cubic graphs in graph theory, revealing new labeling possibilities for these complex structures.

Contribution

It introduces the concept of Cordial labeling for Goldberg Snark graphs and identifies special forms that admit such labelings, expanding understanding of graph labelings.

Findings

Goldberg Snark graphs can be Cordial labeled.

Certain special forms of Goldberg Snark graphs admit Cordial labeling.

The study extends the class of graphs known to have Cordial labelings.

Abstract

In graph theory, a Snark is a connected, bridgeless, Cubic graph that cannot be edge-colored with only three colors. Additionally, to avoid some trivial cases, a Snark is typically required to have a girth of minimum five and a cyclic connectivity of minimum four. In this paper, we investigate the Cordial labeling, for one of the modified structures of Snark graph which is known as Goldberg Snark graph. Moreover, a few special forms of Goldberg Snark graph also admit the Cordial labeling.