NEIGHBOURHOOD DEGREE MATRIX OF A GRAPH
Vol. 9(2) July 2021, No. 18, pp. 206-221
B. BASAVANAGOUD AND PRAVEEN JAKKANNAVAR
In this note, we define a new graph matrix called neighbourhood degree matrix of a graph G and study its properties. The relations connecting this matrix with some degree-based topological indices are investigated. In addition, we present bounds for the spectral radius of neighbourhood degree matrix and neighbourhood degree energy of graphs and we express the neighbourhood degree energy of some transformation graphs in terms of neighbourhood degree energy of the graph considered for the transformation.