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In this paper we obtain an upper bound and also a lower bound for maximum edges of strongly 2 multiplicative graphs of order n. Also we prove that triangular ladder the graph obtained by duplication of an arbitrary edge by a new vertex in path and the graphobtained by duplicating all vertices by new edges in a path and some other graphs are strongly 2 multiplicative

Abstract: A graph G with p vertices is said to be strongly multiplicative if the vertices of G can be labeled with p consecutive positive integers 1, 2, ..., p such that label induced on the edges by the product of labels of end vertices are all distinct. In this paper we investigate strongly multiplicative labeling of some snake related graphs. We prove that alternate triangular snake and alte...

We investigate some new results for strongly multiplicative labeling of graph. We prove that the graph obtained by arbitrary supersubdivision of tree T , grid graph Pn × Pm, complete bipartite graph Km,n, Cn Pm and one-point union of m cycle of length n are strongly multiplicative.

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1  G and ( ) 2  G , under the name first and second multiplicative Zagreb index, respectively. These are define as     ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2...

for a graph $g$ with edge set $e(g)$, the multiplicative sum zagreb index of $g$ is defined as$pi^*(g)=pi_{uvin e(g)}[d_g(u)+d_g(v)]$, where $d_g(v)$ is the degree of vertex $v$ in $g$.in this paper, we first introduce some graph transformations that decreasethis index. in application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum zagreb ...

In this paper we consider graph access structures and we show that such an access structure can be realized by a (strongly) multiplicative monotone span program if and only if the privacy structure contains at least three (resp. four) maximal sets. Thus, we obtain a new family of access structures with an explicit construction that is both ideal and strongly multiplicative. Until now only three...

For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb ...