Harishchandra S. Ramane

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The energy E(G) of a graph G is the sum of absolute values of the eigenvalues of G . Two graphs G1 and G2 are equienergetic if E(G1) = E(G2) . Since 2004, when the concept of equienergetic graphs was introduced, a large number of results on this matter has been obtained. In this paper we briefly outline these results, and give emphasis on the following. If(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)
The distance or D-eigenvalues of a graph G are the eigenvalues of its distance matrix. The distance or D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. Two graphs G1 and G2 are said to be D-equienergetic if ED(G1) = ED(G2). Let F1 be the 5-vertex path, F2 the graph obtained by identifying one vertex of a triangle with(More)
Let G be the connected graph with vertex set V (G) = fv1; v2; : : : ; vpg. The resistance distance between two vertices vi and vj in a connected graph G is the e ective resistance between these two vertices when a battery is assumed to be connected across them and is denoted by r(vi; vj). The resistance of a graph G is equal to the sum of resistance(More)
1. C. Adiga, A. Bayad, I. Gutman, S. A. Srinivas, The minimum covering energy of a graph, Kragujevac Journal of Science, 34(2012), 39-56. 2. R. B. Bapat, Graphs and Matrices, Hindustan Book Agency, 2011. 3. R. B. Bapat, S. Pati, Energy of a graph is never an odd integer, Bulletin of Kerala Mathematics Association, 1(2011), 129-132. 4. J. Bermond, J. Bond,(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.
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