We disprove a conjecture of Estrada and Rodríguez-Velázquez [Phys. Rev. E 71, 056103 (2005)] that if a graph has identical subgraph centrality for all nodes, then the closeness and betweenness centralities are also identical for all nodes.

Abstract The Estrada index of a graph/network is defined as the trace adjacency matrix exponential. It has been extended to other graph-theoretic matrices, such Laplacian, distance, Seidel adjacency, Harary, etc. Here, we describe many these extensions, including new ones, Gaussian, Mittag–Leffler and Onsager ones. More importantly, contextualize all indices in physico-mathematical frameworks w...

Let $G=(V(G),E(G))$ be a simple graph with vertex set $V(G)=\{v_{1},v_{2},\cdots, v_{n}\}$ and edge $E(G)$. The $p$-Sombor matrix $\mathcal{S}_{p}(G)$ of $G$ is the square order $n$ whose $(i,j)$-entry equal to $((d_{i})^{p}+(d_{j})^{p})^{\frac{1}{p}}$ if $v_{i}\sim v_{j}$, 0 otherwise, where $d_{i}$ denotes degree $v_{i}$ in $G$. In this paper, we study relationship between index $SO_{p}(G)$ b...

Several attitudes toward Statistic scales have been proposed in the literature by considering samples of university students but specific scales with cross-cultural validity are not known for teachers. In this study we show the psychometric characteristic of the scale of Attitudes toward the Statistic proposed by Estrada (2002) and Estrada Batanero and Fortuny (2003). The scale was applied to 2...

In this talk we consider some results and open problems from the Chemical Graph Theory, mainly concerning structural indices/properties. The Atom Bond Connectivity index, also known as ABC index was defined by Estrada [4] with relation to the energy of formation of alkanes. It was quickly recognized that this index reflects important structural properties of graphs in general. The ABC index was...