Prime labeling of graphs constructed from wheel graph.

A prime labeling of a simple undirected graph is to assign unique integer labels from the set to each vertex such that any two adjacent vertices in the graph have labels that are relatively prime. Studying prime labeling in graphs can help us understand the structure and properties of graphs and prime labeling has potential applications in cryptography and network security. In this paper we investigate when some graphs that are constructed from wheels are prime graphs.

The extreme vertices of the power graph of a group.

For a fixed finite group , the power graph of was defined to be the simple graph whose vertex set , and edge set . In this paper the extreme vertices of the power graph of abelian groups, dihedral groups and dicyclic groups have been characterized.