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The distance or D-eigenvalues of a graph G are the eigenvalues of its distance matrix. The distance or D-energy E D (G) of the graph G is the sum of the absolute values of its D-eigenvalues. Two graphs G 1 and G 2 are said to be D-equienergetic if E D (G 1) = E D (G 2). Let F 1 be the 5-vertex path, F 2 the graph obtained by identifying one vertex of a… (More)
The Hosoya polynomial is determined for thorn trees, thorn rods, rings, and stars, which are special cases of thorn graphs. By this some earlier results by Bonchev and Klein are generalized. Various distance–based topological indices, namely Wiener index, hyper–Wiener index, Harary index, and reciprocal Wiener index can thus be computed for the classes of… (More)
In this paper, we express the Laplacian polynomial of a graph in terms of the characteristic polynomials of its induced subgraphs. Further the Laplacian polynomial of a regular graph is expressed in terms of derivatives of its characteristic polynomial. In the sequel we obtain the Laplacian polynomial of a complement of a graph in terms of the… (More)
In this paper, the concept of minimum hub distance energy EHd(G) of a connected graph G is introduced and minimum hub distance energies of some standard graphs and a number of wellknown families of graphs are computed. Upper and lower bounds for EHd(G) are also established.
The energy of a graph is equal to the sum of the absolute values of its eigenvalues. This concept was proposed quite some time ago in the paper: I. Gutman, The energy of a graph, Berichte der Mathematisch–Statistischen Sektion im Forschungszentrum Graz 103 (1978) 1–22 (and later on several other occasions). After a long latent period, it now became a… (More)
The energy of a graph is the sum of the absolute values of its eigenvalues. Two graphs are said to be equienergetic if their energies are equal. We show how infinitely many pairs of equienergetic graphs can be constructed, such that these graphs are connected, possess equal number of vertices, equal number of edges, and are not cospectral.