On the determinant of q-distance matrix of a graph

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...

On the spectra of reduced distance matrix of the generalized Bethe trees

Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.

Altan derivatives of a graph

Altan derivatives of polycyclic conjugated hydrocarbons were recently introduced and studied in theoretical organic chemistry. We now provide a generalization of the altan concept, applicable to any graph. Several earlier noticed topological properties of altan derivatives of polycyclic conjugated hydrocarbons are shown to be the properties of all altan derivatives of all graphs. Among these ar...

Resistance matrix and q-Laplacian of a unicyclic graph

The resistance distance between two vertices of a graph can be defined as the effective resistance between the two vertices, when the graph is viewed as an electrical network with each edge carrying unit resistance. The concept has several different motivations. The resistance matrix of a graph is a matrix with its (i, j)-entry being the resistance distance between vertices i and j. We obtain a...

A Note on Strongly Quotient Graphs