منابع مشابه
note 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 کاملComputing the additive degree-Kirchhoff index with the Laplacian matrix
For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.
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 ...
متن کاملCacti with minimum, second-minimum, and third-minimum Kirchhoff indices
Resistance distance was introduced by Klein and Randić. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all pairs of vertices. A graph G is called a cactus if each block of G is either an edge or a cycle. Denote by Cat(n; t) the set of connected cacti possessing n vertices and t cycles. In this paper, we give the first three smallest Kirchhoff indices among gra...
متن کاملThe Quasi-Wiener and the Kirchhoff Indices Coincide
In 1993 two novel distance-based topological indices were put forward. In the case of acyclic molecular graphs both are equal to the Wiener index, but both differ from it if the graphs contain cycles. One index is defined (Mohar, B.; Babić, D.; Trinajstić, N. J. Chem. Inf. Comput. Sci. 1993, 33, 153-154) in terms of eigenvalues of the Laplacian matrix, whereas the other is conceived (Klein, D. ...
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ژورنال
عنوان ژورنال: Filomat
سال: 2015
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1508869m