On the Kirchhoff index of the complement of a bipartite graph
Qingying Deng,Haiyan Chen +1 more
TLDR
The Kirchhoff index of a bipartite graph G is defined as Kf (G ) = 1 2 ∑ i = 1 n ∑ j = 1n r ij, where r is the resistance distance between v i and v j as mentioned in this paper.About:
This article is published in Linear Algebra and its Applications.The article was published on 2013-07-01 and is currently open access. It has received 21 citations till now. The article focuses on the topics: Complement graph & Edge-transitive graph.read more
Citations
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Book ChapterDOI
An Introduction to the Theory of Graph Spectra: Spectral techniques
TL;DR: In this article, the authors introduce the concept of graph operations and modifications, and characterizations of spectra by characterizations by spectra and one eigenvalue, and Laplacians.
Journal ArticleDOI
Minimizing Kirchhoff index among graphs with a given vertex bipartiteness
Jia-Bao Liu,Xiang-Feng Pan +1 more
TL;DR: This paper characterize the graph having the minimum Kf(G) values among graphs with a fixed number n of vertices and fixed vertex bipartiteness, 1 ź v b ź n - 3 .
Journal ArticleDOI
Complete characterization of bicyclic graphs with minimal Kirchhoff index
TL;DR: This paper completely characterize the bicyclic graphs of order n ?
Journal ArticleDOI
Resistance distance-based graph invariants of subdivisions and triangulations of graphs
Yujun Yang,Douglas J. Klein +1 more
TL;DR: In this article, the authors study three resistance distance-based graph invariants: the Kirchhoff index, and two modifications, namely, the multiplicative degree-Kirchhoff indices and the additive degree-kirchhoffs index.
Journal ArticleDOI
On extremal bipartite unicyclic graphs
Qingying Deng,Haiyan Chen +1 more
TL;DR: In this paper, the authors consider the extremal graphs in U n + with respect to both the Estrada index of themselves and the Kirchhoff index of their complements.
References
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MonographDOI
Algebraic graph theory
TL;DR: In this article, the authors introduce algebraic graph theory and show that the spectrum of a graph can be modelled as a graph graph, and the spectrum can be represented as a set of connected spanning trees.
Book
An Introduction to the Theory of Graph Spectra
TL;DR: In this article, the authors explore the theory of graph spectra, a topic with applications across a wide range of subjects, including computer science, quantum chemistry, electrical engineering and electrical engineering.
Book ChapterDOI
An Introduction to the Theory of Graph Spectra: Spectral techniques
TL;DR: In this article, the authors introduce the concept of graph operations and modifications, and characterizations of spectra by characterizations by spectra and one eigenvalue, and Laplacians.
Journal ArticleDOI
The quasi-wiener and the kirchhoff indices coincide
Ivan Gutman,Bojan Mohar +1 more
TL;DR: It is demonstrated that the quasi-Wiener and Kirchhoff indices of all graphs coincide.
Journal ArticleDOI
Resistance distance and Laplacian spectrum
TL;DR: In this paper, the Laplacian eigenvalues and eigenvectors of a connected, molecular graph G are expressed in terms of the resistance matrix of the graph.