Resistance distance, Kirchhoff index, and Kemeny's constant in flower graphs

Kemeny's constant and Kirchhoffian indices for a family of non-regular graphs

We find closed form formulas for Kemeny's constant and its relationship with two Kirchhoffian indices for some composite graphs that use as basic building block a graph endowed with one of several symmetry properties.

Kemeny's constant and the Kirchhoff index for the cluster of highly symmetric graphs

We find closed form formulas for the Kemeny's constant and the Kirchhoff index for the cluster $G_1\{G_2\}$ of two highly symmetric graphs $G_1$, $G_2$, in terms of the parameters of the original graphs. We also discuss some necessary conditions for a graph to be highly symmetric.

Spectra, hitting times, and resistance distances of $q$-subdivision graphs

Graph operations or products play an important role in complex networks. In this paper, we study the properties of $q$-subdivision graphs, which have been applied to model complex networks. For a simple connected graph $G$, its $q$-subdivision graph $S_q(G)$ is obtained from $G$ through replacing every edge $uv$ in $G$ by $q$ disjoint paths of length 2, with each path having $u$ and $v$ as its ends. We derive explicit formulas for many quantities of $S_q(G)$ in terms of those corresponding to $G$, including the eigenvalues and eigenvectors of normalized adjacency matrix, two-node hitting time,…

某些图的 $k$-凝聚中的电阻距离

Resistance distance in $k$-coalescence of certain graphs

本文研究完全图的 $k$-凝聚中的电阻距离，给出其与多种 Kirchhoff 型指数的联系，并推广到特定图及风车图、菠萝图等应用。

两个图的中心点联图与中心边联图中的电阻距离和 Kirchhoff 指数

Resistance distance and Kirchhoff index in central vertex join and central edge join of two graphs

本文研究两类图运算的电阻距离与 Kirchhoff 指数，推导中心点联图和中心边联图的计算公式，并给出中心图的相关不变量。

Tree formulas, mean first passage times and Kemeny's constant of a Markov chain

In this paper, we aim to provide probabilistic and combinatorial insights into tree formulas for the Green function and hitting probabilities of Markov chains on a finite state space. These tree formulas are closely related to loop-erased random walks by Wilson's algorithm for random spanning trees, and to mixing times by the Markov chain tree theorem. Let $m_{ij}$ be the mean first passage time from $i$ to $j$ for an irreducible chain with finite state space $S$ and transition matrix $(p_{ij}; i, j \in S)$. It is well-known that $m_{jj} = 1/π_j = Σ^{(1)}/Σ_j$, where $π$ is the stationary dist…