Distance regularity in direct-product graphs

Distance regularity in direct-product graphs

K e y w o r d s D i s t a n c e r e g u l a r graphs, Direct product. 1. I N T R O D U C T I O N E v e r y c o n n e c t e d g r a p h is r e p r e s e n t a b l e by m e a n s o f a level diagram (cf. [1]) as follows. C h o o s e a v e r t e x u, a n d le t i t be t h e sole r e s iden t of level zero. T h e ve r t i c e s on level i a re p rec i se ly t h o s e w h o s e d i s t a n c e f r o...

Distance in the Direct Product of Graphs

Product 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.

Generalized Degree Distance of Strong Product of Graphs

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

Distance-based topological indices of tensor product of graphs

Let G and H be connected graphs. The tensor product G + H is a graph with vertex set V(G+H) = V (G) X V(H) and edge set E(G + H) ={(a , b)(x , y)| ax ∈ E(G) & by ∈ E(H)}. The graph H is called the strongly triangular if for every vertex u and v there exists a vertex w adjacent to both of them. In this article the tensor product of G + H under some distancebased topological indices are investiga...