A graph G = (V, E) with n vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding n such that the labels of each pair of adjacent vertices are relatively prime. A graph G which admits prime labeling is called a prime graph. In the present work we investigate some classes of graphs which admit prime labeling. We also introduce the concept of k−prime labeling and investigate some results concern to it. This work is a nice combination of graph theory and elementary number theory.
We investigate prime labeling for some graphs resulted from switching of a vertex. We discuss switching invariance of some prime graphs and prove that the graphs obtained by switching of a vertex in and n P 1,n K admit prime labeling.Moreover we discuss prime labeling for the graph obtained by switching of vertex in wheel .n W
In the present work we investigate some classes of graphs and disjoint union of some classes of graphs which admit prime labeling. We also investigate prime labeling of a graph obtained by identifying two vertices of two graphs. We also investigate prime labeling of a graph obtained by identifying two edges of two graphs. Prime labeling of a prism graph is also discussed. We show that a wheel graph of odd order is switching invariant. A necessary and sufficient condition for the complement of n W to be a prime graph is investigated.
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