Subdivision Graph, Power and Line Graph of a Soft Graph

Abstract

Soft set is a classification of elements of the universe with respect to some given set of parameters. It is a new approach for modeling vagueness and uncertainty. The concept of soft graph is used to provide a parameterized point of view for graphs. In this paper we introduce the concepts of subdivision graph, power and line graph of a soft graph and investigate some of their properties.

Computation of wiener polynomial and index of line subdivision friendship and line subdivision bifriendship graphs using matlab program

“…A Subdivision graph [39,16] of a graph G is a graph with adding vertex of degree two for any edge of G. A Line graph [34,31] of G L(G) is a graph with vertices as the edges of G and the two vertices of L(G) are adjacency if and only if the two edges have common in G. A graph G is connected if every two vertices are joint by path denoted by u−v and the length of the path denoted by p(u,v) and the shortest path between two vertices is called a distance, denoted by d(u, v), define as d (u, v) = min{P (u, v) : u, v ∈ V (G)} and the diameter of G denoted by δ (G), define as δ (G) = max{d (u, v) : u, v ∈ V (G)}. The Wiener polynomial [13,14] of a graph G define as…”