Radio Analytic Mean Graceful Number of Star and Bistar Related Graphs

Abstract

In this paper, we introduce the concept of star and Bistar-related graceful graphs that satisfy the radio analytic mean condition. Specifically, a radio analytic mean labeling of a graph G=(V,E) is defined
as a function f:V(G)→N f: V(G) }such that for any two vertices u and v, the following condition holds
d(u,v) + ⌈|〖θ(u)〗^2-〖θ(v)〗^2 |/2⌉ ≥ 1+ diam (G) . where d(u,v)d(u, v)d(u,v) represents the distance between any two vertices u and v in G, and diam(G) is the diameter of the graph G.The radio analytic mean number ramgn(f) is the maximum integer allocated to any node of G, and this node is referred to as the radio analytic mean graceful number.In this article, we investigate the ramgn of certain star and Bistar-related graphs, exploring how these graphs satisfy the radio analytic mean condition and examining their properties.Where d(u,v) is distance between any two nodes of G. A radio analytic mean number ramgn (f) is maximum integer allocated to any node of G. In this node is called radio analytic mean graceful number. In this article we investigate ramgn certain star and Bistar Related graphs.