Graph energy is defined to be the p -norm of adjacency matrix associated graph for = 1 elaborated as sum absolute eigenvalues matrix. The graph’s spectral radius represents matrix’s largest eigenvalue. Applications energies and radii can found in both molecular computing computer science. On similar lines, Inverse Sum Indeg, ( ISI ) energies, constructed. This article’s main focus generalized s...

A graph containment problem is to decide whether one graph can be modified into some other graph by using a number of specified graph operations. We consider edge deletions, edge contractions, vertex deletions and vertex dissolutions as possible graph operations permitted. By allowing any combination of these four operations we capture the following ten problems: testing on (induced) minors, (i...

In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exac...

edge distance-balanced graphs are graphs in which for every edge $e = uv$ the number of edges closer to vertex $u$ than to vertex $v$ is equal to the number of edges closer to $v$ than to $u$. in this paper, we study this property under some graph operations.

Graph complexity measures like tree-width, clique-width, NLC-width and rank-width are important because they yield Fixed Parameter Tractable algorithms. Rank-width is based on ranks of adjacency matrices of graphs over GF(2). We propose here algebraic operations on graphs that characterize rank-width. For algorithmic purposes, it is important to represent graphs by balanced terms. We give a uni...

The nullity of a graph G is the multiplicity zero as an eigenvalue its adjacency matrix. An assignment weights to vertices graph, that satisfies sum condition over neighbors each vertex, and uses maximum number independent variables denoted by high weighting graph. This applicable tool used determine Two types graphs are defined, change their nullities studied, namely, G+ab constructed from add...