Abstract. In this paper the idea of sum distance which is a metric, in a fuzzy graph is introduced. The concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied using this metric. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterization of self centered complete fuzzy graph is obtained and conditions under which...

For a (molecular) graph, the multiplicative Zagreb indices ∏ 1-index and ∏ 2index are multiplicative versions of the ordinary Zagreb indices (M1-index and M2index). In this note we report several sharp upper bounds for ∏ 1-index in terms of graph parameters including the order, size, radius, Wiener index and eccentric distance sum, and upper bounds for ∏ 2-index in terms of graph parameters inc...

Let G be a digraph. For two vertices u and v in G, the distance d(u, v) from u to v in G is the length of the shortest directed path from u to v. The eccentricity e(v) of v is the maximum distance of v to any other vertex of G. A vertex u is an eccentric vertex of v if the distance from v to u is equal to the eccentricity of v. The eccentric digraph ED(G) of G is the digraph that has the same v...

‎the second multiplicative zagreb coindex of a simple graph $g$ is‎ ‎defined as‎: ‎$${overline{pi{}}}_2left(gright)=prod_{uvnotin{}e(g)}d_gleft(uright)d_gleft(vright),$$‎ ‎where $d_gleft(uright)$ denotes the degree of the vertex $u$ of‎ ‎$g$‎. ‎in this paper‎, ‎we compare $overline{{pi}}_2$-index with‎ ‎some well-known graph invariants such as the wiener index‎, ‎schultz‎ ‎index‎, ‎eccentric co...

Inequalities provide a way to study topological indices relatively. There are two major classes of topological indices: degree-based and distance-based indices. In this paper we provide a relative study of these classes and derive inequalities between degree-based indices such as Randić connectivity, GA, ABC, and harmonic indices and distance-based indices such as eccentric connectivity, connec...

The corona product G ◦ H of two graphs G and H is obtained by taking one copy of G and |V (G)| copies of H; and by joining each vertex of the i-th copy of H to the i-th vertex of G, where 1 ≤ i ≤ |V (G)|. In this paper, exact formulas for the eccentric distance sum and the edge revised Szeged indices of the corona product of graphs are presented. We also study the conditions under which the cor...

Let G=(V,A) be a digraph. The eccentricity e(u) of a vertex u is the maximum distance from u to any other vertex in G. A vertex v in G is an eccentric vertex of u if the distance from u to v equals e(u). The eccentric digraph ED(G) of a digraph G has the same vertex set as G and has arcs from a vertex v to its eccentric vertices. In this paper we present several results on the eccentric digraph...

Let G be a nontrivial connected graph. The distance between two vertices u and v of G is the length of a shortest u-v path in G. Let u be a vertex in G. A vertex v is an eccentric vertex of u if d(u, v) = e(u), that is every vertex at greatest distance from u is an eccentric vertex of u. A vertex v is an eccentric vertex of G if v is an eccentric vertex of some vertex of G. Consequently, if v i...