منابع مشابه
Kirchhoff index of composite graphs
Let G 1 + G 2 , G 1 • G 2 and G 1 {G 2 } be the join, corona and cluster of graphs G 1 and G 2 , respectively. In this paper, Kirchhoff index formulae of these composite graphs are given.
متن کاملnote on degree kirchhoff index of graphs
the degree kirchhoff index of a connected graph $g$ is defined as the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices, where $d_i$ is the degree of the $i$-th vertex, and $r_{ij}$ the resistance distance between the $i$-th and $j$-th vertex of $g$. bounds for the degree kirchhoff index of the line and para-line graphs are determined. the special case of regular grap...
متن کاملOn the Kirchhoff Index of Graphs
Let G be a connected graph of order n with Laplacian eigenvalues μ1 ≥ μ2 ≥ . . .≥ μn−1 > μn = 0. The Kirchhoff index of G is defined as Kf = Kf(G) = n∑n−1 k=1 1/μk. In this paper. we give lower and upper bounds on Kf of graphs in terms on n, number of edges, maximum degree, and number of spanning trees. Moreover, we present lower and upper bounds on the Nordhaus–Gaddum-type result for the Kirch...
متن کاملMaximizing Kirchhoff index of unicyclic graphs with fixed maximum degree
The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. Its considerable applications are found in a variety of fields. In this paper, we determine the maximum value of Kirchhoff index among the unicyclic graphs with fixed number of vertices and maximum degree, and characterize the corresponding extremal graph.
متن کاملFurther Results regarding the Degree Kirchhoff Index of Graphs
Let G be a connected graph with vertex set V.G/. The degree Kirchhoff index of G is defined as S .G/D P fu;vg V.G/ d.u/d.v/R.u;v/, where d.u/ is the degree of vertex u, and R.u;v/ denotes the resistance distance between vertices u and v. In this paper we obtain some upper and lower bounds for the degree Kirchhoff index of graphs. We also obtain some bounds for the Nordhaus-Gaddum-type result fo...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2009.03.007