On the eccentricity energy of complete mutipartite graph

Eccentricity energy change of complete multipartite graphs due to edge deletion

The eccentricity matrix $\varepsilon(G)$ of a graph $G$ is obtained from the distance matrix of $G$ by retaining the largest distances in each row and each column, and leaving zeros in the remaining ones. The eccentricity energy of $G$ is sum of the absolute values of the eigenvalues of $\varepsilon(G)$. Although the eccentricity matrices of graphs are closely related to the distance matrices of graphs, a number of properties of eccentricity matrices are substantially different from those of the distance matrices. The change in eccentricity energy of a graph due to an edge deletion is one such…

一类双块图的离心率矩阵的惯性与谱对称性

Inertia and spectral symmetry of the eccentricity matrices of a class of bi-block graphs

本文研究包含树的双块图子类B的离心率矩阵，确定其惯性，证明直径大于3时特征值关于原点对称当且仅当直径为奇数，并证明矩阵不可约。

$\mathcal{C}$-图的离心率谱性质

Eccentricity spectral properties of $\mathcal{C}$-graphs

本文研究特殊余图类 $\mathcal{C}$-图的离心率矩阵谱性质，确定其不可约性、惯性，并给出一个无离心率特征值的区间。

图的 $H$-join 的离心率矩阵的谱

Spectra of eccentricity matrix of $H$-join of graphs

本文研究了图的 $H$-join 的离心率矩阵，求出了其离心率谱和特征多项式，并推广了多项已有结果。

The Steiner $k$-radius and Steiner $k$-diameter of connected graphs for $k\geq 4$

Given a connected graph $G=(V,E)$ and a vertex set $S\subset V$, the {\em Steiner distance} $d(S)$ of $S$ is the size of a minimum spanning tree of $S$ in $G$. For a connected graph $G$ of order $n$ and an integer $k$ with $2\leq k \leq n$, the $k$-eccentricity of a vertex $v$ in $G$ is the maximum value of $d(S)$ over all $S\subset V$ with $|S|=k$ and $v\in S$. The minimum $k$-eccentricity, ${srad}_k(G)$, is called the $k$-radius of $G$ while the maximum $k$-eccentricity, ${sdiam}_k(G)$, is called the $k$-diameter of $G$. In 1990, Henning, Oellermann, and Swart [\textit{Ars Combinatoria} \tex…

On the difference between the eccentric connectivity index and eccentric distance sum of graphs

The eccentric connectivity index of a graph $G$ is $ξ^c(G) = \sum_{v \in V(G)}\varepsilon(v)°(v)$, and the eccentric distance sum is $ξ^d(G) = \sum_{v \in V(G)}\varepsilon(v)D(v)$, where $\varepsilon(v)$ is the eccentricity of $v$, and $D(v)$ the sum of distances between $v$ and the other vertices. A lower and an upper bound on $ξ^d(G) - ξ^c(G)$ is given for an arbitrary graph $G$. Regular graphs with diameter at most $2$ and joins of cocktail-party graphs with complete graphs form the graphs that attain the two equalities, respectively. Sharp lower and upper bounds on $ξ^d(T) - ξ^c(T)$ are gi…