The Multiplicative Version of Degree Distance and the Multiplicative Version of Gutman Index of Strong Product of some Graphs
نویسنده
چکیده
In this paper, we present the exact formulae for the multiplicative version of degree distance and the multiplicative version of Gutman index of strong product of graphs in terms of other graph invariants including the Wiener index and Zagreb index. Finally, we apply our results to the multiplicative version of degree distance and the multiplicative version of Gutman index of open and closed fence graphs. AMS subject classification:
منابع مشابه
Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs
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...
متن کاملThe Multiplicative Versions of the Reciprocal Degree Distance and Reciprocal Gutman Index of Some Graph Products
In this paper, we provide exact value of the multiplicative version of the reciprocal degree distance and the multiplicative version of the reciprocal Gutman index of Cartesian product of complete graphs. Also, we establish sharp upper bounds for the multiplicative version of the reciprocal degree distance and multiplicative version of the reciprocal Gutman index of strong product of graphs.
متن کاملThe ratio and product of the multiplicative Zagreb indices
The first multiplicative Zagreb index $Pi_1(G)$ is equal to the product of squares of the degree of the vertices and the second multiplicative Zagreb index $Pi_2(G)$ is equal to the product of the products of the degree of pairs of adjacent vertices of the underlying molecular graphs $G$. Also, the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of the sum...
متن کاملProduct version of reciprocal degree distance of composite graphs
A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.
متن کاملOn multiplicative Zagreb indices of graphs
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...
متن کامل