Minimizing Kirchhoff index among graphs with a given vertex bipartiteness

JB Liu, XF Pan - Applied mathematics and computation, 2016 - Elsevier
The resistance distance between any two vertices of a graph G is defined as the effective
resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index …

[HTML][HTML] Complete characterization of bicyclic graphs with minimal Kirchhoff index

JB Liu, XF Pan, L Yu, D Li - Discrete Applied Mathematics, 2016 - Elsevier
The resistance distance between any two vertices of a graph G is defined as the network
effective resistance between them if each edge of G is replaced by a unit resistor. The …

[HTML][HTML] Resistance distance-based graph invariants of subdivisions and triangulations of graphs

Y Yang, DJ Klein - Discrete Applied Mathematics, 2015 - Elsevier
We study three resistance distance-based graph invariants: the Kirchhoff index, and two
modifications, namely, the multiplicative degree-Kirchhoff index and the additive degree …

[HTML][HTML] On the Kirchhoff index of graphs with diameter 2

JL Palacios - Discrete Applied Mathematics, 2015 - Elsevier
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[HTML][HTML] On the Ihara zeta function and resistance distance-based indices

M Somodi - Linear Algebra and its Applications, 2017 - Elsevier
On the Ihara zeta function and resistance distance-based indices - ScienceDirect Skip to main
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[HTML][HTML] On the Kirchhoff index of bipartite graphs with given diameters

X Jiang, W He, Q Liu, J Li - Discrete Applied Mathematics, 2020 - Elsevier
In this paper, among all the bipartite graphs with diameter 2 and 3, we characterize the
graphs which have the largest and the smallest Kirchhoff index. Moreover, we characterize …

[HTML][HTML] On extremal bipartite unicyclic graphs

Q Deng, H Chen - Linear Algebra and Its Applications, 2014 - Elsevier
Let U n+ be the set of connected bipartite unicyclic graphs with n vertices. Here we consider
the extremal graphs in U n+ with respect to both the Estrada index of themselves and the …

Ordering connected graphs by their Kirchhoff indices

K Xu, KC Das, XD Zhang - International Journal of Computer …, 2016 - Taylor & Francis
The Kirchhoff index Kf (G) of a graph G is the sum of resistance distances between all
unordered pairs of vertices, which was introduced by Klein and Randić. In this paper, we …

A note on the Kirchhoff and additive degree-Kirchhoff indices of graphs

Y Yang, DJ Klein - Zeitschrift für Naturforschung A, 2015 - degruyter.com
Two resistance-distance-based graph invariants, namely, the Kirchhoff index and the
additive degree-Kirchhoff index, are studied. A relation between them is established, with …

On the minimum Kirchhoff index of graphs with a given vertex k-partiteness and edge k-partiteness

W He, H Li, S Xiao - Applied Mathematics and Computation, 2017 - Elsevier
The Kirchhoff index of a connected graph is the sum of the resistance distance between all
unordered pairs of vertices and may also be expressed by its Laplacian eigenvalues. The …