相关论文: Extremal octagonal chains with respect to the Kirc…
The Wiener index of a (hyper)graph is calculated by summing up the distances between all pairs of vertices. We determine the maximum possible Wiener index of a connected $n$-vertex $k$-uniform hypergraph and characterize for every~$n$ all…
The orthogonality graph of an Okubo algebra with isotropic norm over an arbitrary field $\mathbb{F}$ is considered. Its connected components are described, and their diameters are computed. It is shown that there exist at most two shortest…
The number of spanning trees in a graph $G$ is the total number of distinct spanning subgraphs of $G$ that are trees. In this paper we characterize the unique graph with a prescribed vertex (resp. edge) connectivity, minimum degree and…
We consider the graph $G_n$ with vertex set $V(G_n) = \{ 1, 2, \ldots, n\}$ and $\{i,j\} \in E(G_n)$ if and only if $0<|i-j| \leq 2$. We call $G_n$ the straight linear 2-tree on $n$ vertices. Using $\Delta$--Y transformations and identities…
The Wiener index of a graph is the sum of all the distances between any pair of vertices. We aim to describe graphs which minimize the Wiener index among all unicyclic graphs with fixed girth and given degree sequence. Depending on where…
By revisiting the Kirchhoff's Matrix-Tree Theorem, we give an exact formula for the number of spanning trees of a graph in terms of the quantum relative entropy between the maximally mixed state and another state specifically obtained from…
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…
The edge-Wiener index $W_e(G)$ of a connected graph $G$ is the sum of distances between all pairs of edges of $G$. A connected graph $G$ is said to be a cactus if each of its blocks is either a cycle or an edge. Let $\mathcal{G}_{n,t}$…
The atom-bond connectivity (ABC) index is a well-known degree-based molecular structure descriptor with a variety of chemical applications. In 2010 Graovac and Ghorbani introduced a distance-based analog of this index, the Graovac-Ghorbani…
Assessing and improving the robustness of a graph $G$ are critical steps in network design and analysis. To this end, we consider the optimisation problem of removing $k$ edges from $G$ such that the resulting graph has minimal robustness,…
The Wiener index $W(G)$ of a graph $G$ is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of $G$. The diameter $D(G)$ of $G$ is the maximum distance between all pairs of…
Understanding how the cycles of a graph or digraph behave in general has always been an important point of graph theory. In this paper, we study the question of finding a set of $k$ vertex-disjoint cycles (resp. directed cycles) of distinct…
In network theory, the concept of effective resistance is a distance measure on a graph that relates the global network properties to individual connections between nodes. In addition, the Kron reduction method is a standard tool for…
The \emph{thinness} of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Graphs with thinness at most two include, for example, bipartite convex graphs. Many…
The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle-free…
Let $m$ be a positive integer. Brualdi and Hoffman proposed the problem to determine the (connected) graphs with maximum spectral radius in a given graph class and they posed a conjecture for the class of graphs with given size $m$. After…
A vertex k-ranking is a labeling of the vertices of a graph with integers from 1 to k so any path connecting two vertices with the same label will pass through a vertex with a greater label. The rank number of a graph is defined to be the…
Let $G$ be a connected graph. The revised edge Szeged index of $G$ is defined as $Sz^{\ast}_{e}(G)=\sum\limits_{e=uv\in E(G)}(m_{u}(e|G)+\frac{m_{0}(e|G)}{2})(m_{v}(e|G)+\frac{m_{0}(e|G)}{2})$, where $m_{u}(e|G)$ (resp., $m_{v}(e|G)$) is…
For any real $\alpha \in [0,1]$, Nikiforov defined the $A_\alpha$-matrix of a graph $G$ as $A_\alpha(G)=\alpha D(G)+(1-\alpha)A(G)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the diagonal matrix of vertex degrees of $G$,…
The Mostar index of a connected graph \(G\) is defined as \[ Mo(G)=\sum_{uv\in E(G)}\bigl|n_u(uv)-n_v(uv)\bigr|, \] where for an edge \(e=uv\), \(n_u(e)\) denotes the number of vertices of \(G\) that are closer to \(u\) than to \(v\). In…