For a simple connected graph G, Eccentric connectivity index denoted by ( ) c G 7 is defined as: ( ) ( ) ( ( ) ( )) c i V G G E i d i 7 , where E(i) is the eccentricity of vertex i, d(i) is the degree of vertex i and V(G) is the set of vertices of G. Eccentricity of vertex i in a graph G is the path length from verte i to vertex j that is farthest from i. In this paper, an algorithm is presente...

Relation on a set is simple mathematical model to which many real-life data can be connected. A binary relation always represented by digraph. Topology generated relations the . In this direction, study will consider different classical categories of topological spaces whose topology defined adjacency and reachability vertex directed graph. This paper analyses some properties these topologies s...

A tournament is a directed graph T such that every pair of vertices connected by an arc. feedback vertex set S in − acyclic. We consider the Feedback Vertex Set problem tournaments. Here, input and weight function w : V ( ) → N, task to find minimizing = ∑ v∈S v ). Rounding optimal solutions natural LP-relaxation this yields simple 3-approximation algorithm. This has been improved 2.5 Cai et al...

For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M1(G) = ∑ v∈V (G) dG(v) 2 where dG(v) is the degree of vertex v in G. The alternative expression for M1(G) is ∑ uv∈E(G)(dG(u)+dG(v)). Very recently, Eliasi, Iranmanesh and Gutman [7] introduced a new graphical invariant ∏∗ 1(G) = ∏ uv∈E(G)(dG(u) + dG(v)) as the multiplicative version of ...