Abstract
ABSTRACT For a simple connected graph G, let , , and , respectively, are the distance matrix, the diagonal matrix of the vertex transmissions, distance Laplacian matrix and the distance signless Laplacian matrix. The generalized distance matrix of G is the convex linear combinations of and and is defined as , for . As and , this matrix reduces to merging the distance spectral and distance signless Laplacian spectral theories. Let be the eigenvalues of and let be the generalized distance spectral spread of the graph G. In this paper, we obtain bounds for the generalized distance spectral spread . We also obtain a relation between the generalized distance spectral spread and the distance spectral spread . Further, we obtain lower bounds for of bipartite graphs involving different graph parameters and we characterize the extremal graphs for some cases. We also obtain lower bounds for in terms of clique number and independence number of the graph G and characterize the extremal graphs for some cases.
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