EVEN RADIO MEAN GRACEFUL LABELING ON DEGREE SPLITTING OF SNAKE RELATED GRAPHS

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 173

Abstract

A radio mean labeling of a connected graph G is an injection $\phi$ from the vertex set V(G) to N such that the condition $d(u, v)+ \Bigg \lceil \frac{ {\phi(u) + \phi(v)} }{ 2 }\Bigg \rceil $ $\geq 1 + diam(G)$ holds for any two distinct vertices u and v of G. A graph which admits radio mean labeling is called radio mean graph. The radio mean number of $\phi$, rmn$(\phi)$, is the maximum number assigned to any vertex of G. The radio mean number of G, rmn(G), is the minimum value of rmn$(\phi)$ taken over all radio mean labeling $\phi$ of G. In this paper we introduce a new concept even radio mean graceful labeling and we investigate the even radio mean graceful labeling on degree splitting of snake related graphs.

Keywords and Phrases

Radio mean graceful labeling, even radio mean graceful labeling, degree splitting graph, triangular snake graph, quadrilateral snake graph.

A.M.S. subject classification

05C78.

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