Further Results on Resistance Distance and Kirchhoff Index in Electric Networks
نویسندگان
چکیده
منابع مشابه
Some Results of Resistance Distance and Kirchhoff Index Based on R-Graph
The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a (unit) resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices in G. For a graph G, let R(G) be the graph obtained from G by adding a new vertex co...
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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...
متن کاملthe resistance distance and the kirchhoff index of the $k$-th semi total point graphs
the $k$-th semi total point graph $r^k(g)$ of a graph $g$, is a graph obtained from $g$ by adding $k$ vertices corresponding to each edge and connecting them to endpoint of edge considered. in this paper, we obtain formulae for the resistance distance and kirchhoff index of $r^k(g)$.
متن کاملTHE RESISTANCE DISTANCE AND KIRCHHOFF INDEX OF THE k-TH SEMI-TOTAL POINT GRAPHS
The k-th semi-total point graph R(G) of a graph G, is a graph obtained from G by adding k vertices corresponding to each edge and connecting them to the endpoints of the edge considered. In this paper, we obtain formulas for the resistance distance and Kirchhoff index of R(G).
متن کاملOn hyper-Kirchhoff index
The hyper-Kirchhoff index is introduced when the hyper-Wiener operator is applied to the resistance-distance matrix of a connected graph. We give lower and upper bounds for the hyper-Kirchhoff index, and determine the n-vertex unicyclic graphs with the smallest, the second and the third smallest as well as the largest, the second and the third largest hyper-Kirchhoff indices for n ≥ 5. We also ...
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ژورنال
عنوان ژورنال: Discrete Dynamics in Nature and Society
سال: 2016
ISSN: 1026-0226,1607-887X
DOI: 10.1155/2016/4682527