Some Results On Q-Integral Graphs

Some results on the energy of the minimum dominating distance signless Laplacian matrix assigned to graphs

Let G be a simple connected graph. The transmission of any vertex v of a graph G is defined as the sum of distances of a vertex v from all other vertices in a graph G. Then the distance signless Laplacian matrix of G is defined as D^{Q}(G)=D(G)+Tr(G), where D(G) denotes the distance matrix of graphs and Tr(G) is the diagonal matrix of vertex transmissions of G. For a given minimum dominating se...

Spectra of Some New Graph Operations and Some New Class of Integral Graphs

In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.

On the edge and total GA indices of some graphs

Some families of integral graphs

A graph is called integral if all its eigenvalues (of the adjacency matrix) are integers. In this paper, the graphs K1,r •Kn , r ∗Kn , K1,r • Km,n , r ∗ Km,n and the tree K1,s • T (q, r,m, t) are defined. We determine the characteristic polynomials of these graphs and also obtain sufficient and necessary conditions for these graphs to be integral. Some sufficient conditions are found by using t...

Matching Integral Graphs of Small Order

In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...