Related papers: Splice Graphs and Their Topological Indices

The weighted Szeged index and the weighted vertex-PI index of a connected graph $G$ are defined as $wSz(G) = \sum_{e=uv \in E(G)} (deg (u) + deg (v))n_u(e)n_v(e)$ and $wPI_v(G) = \sum_{e=uv \in E(G)} (deg(u) + deg(v))( n_u(e) + n_v(e))$,…

For a molecular graph, the first multiplicative Zagreb index $\Pi_1$ is equal to the product of the square of the degree of the vertices, while the second multiplicative Zagreb index $\Pi_2$ is equal to the product of the endvertex degree…

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…

The first Zagreb index of a graph $G$ is the sum of squares of the vertex degrees in a graph and the second Zagreb index of $G$ is the sum of products of degrees of adjacent vertices in $G$. The imbalance of an edge in $G$ is the numerical…

For a graph $G$, the first multiplicative Zagreb index $\prod_1(G) $ is the product of squares of vertex degrees, and the second multiplicative Zagreb index $\prod_2(G) $ is the product of products of degrees of pairs of adjacent vertices.…

The connective eccentric index of a graph is a topological index involving degrees and eccentricities of vertices of the graph. In this paper, we have studied the connective eccentric index for double graph and double cover. Also we give…

The first Zagreb index of a graph $G$ is the sum of the square of every vertex degree, while the second Zagreb index is the sum of the product of vertex degrees of each edge over all edges. In our work, we solve an open question about…

For a (molecular) graph, the first multiplicative Zagreb index $\prod_1(G) $ is the product of the square of every vertex degree, and the second multiplicative Zagreb index $\prod_2(G) $ is the product of the products of degrees of pairs of…

The edge Szeged index of a graph $G$ is defined as $Sz_{e}(G)=\sum\limits_{uv\in E(G)}m_{u}(uv|G)m_{v}(uv|G)$, where $m_{u}(uv|G)$ (resp., $m_{v}(uv|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the…

Szeged, PI and Mostar indices are some of the most investigated distance-based molecular descriptors. Recently, many different variations of these topological indices appeared in the literature and sometimes they are all together called…

The first Zagreb index $M_{1}$ of a graph is defined as the sum of the square of every vertex degree, and the second Zagreb index $M_{2}$ of a graph is defined as the sum of the product of vertex degrees of each pair of adjacent vertices.…

The distance $d(u,v)$ between the vertices $u$ and $v$ of a connected graph $G$ is defined as the number of edges in a minimal path connecting them. The \emph{transmission} of a vertex $v$ of $G$ is defined by $\sigma(v)=\sum\limits_{u\in…

The revised Szeged index of a graph $G$ is defined as $Sz^*(G)=\sum_{e=uv \in E}(n_u(e)+ n_0(e)/2)(n_v(e)+ n_0(e)/2),$ where $n_u(e)$ and $n_v(e)$ are, respectively, the number of vertices of $G$ lying closer to vertex $u$ than to vertex…

The first Zagreb index $M_{1}(G)$ is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index $M_{2}(G)$ is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying…

Let $G$ be a finite group. The intersection graph of $G$ is a graph whose vertex set is the set of all proper non-trivial subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $H\cap K \neq \{e\}$, where $e$ is…

Let $G = (V, E)$ be a graph. The first Zagreb index and the forgotten topological index of a graph $G$ are defined respectively as $\sum_{u \in V} d^2(u)$ and $\sum_{u \in V} d^3(u)$, where $d(u)$ is the degree of vertex $u$ in $G$. If the…

In theoretical chemistry molecular structure descriptors are used for modeling physico-chemical, pharmacological, toxicologic, biological and other properties of chemical compounds. In this paper we study distance-based graph invariants and…

The \emph{eccentricity} of a vertex $u$ in a graph $G$, denoted by $e_G(u)$, is the maximum distance from $u$ to other vertices in $G$. We study extremal problems for the average eccentricity and the first and second Zagreb eccentricity…

We perform a detailed statistical study of the distribution of topological and spectral indices on random graphs $G=(V,E)$ in a wide range of connectivity regimes. First, we consider degree-based topological indices (TIs), and focus on two…

Let $G = (V, E)$ be a graph. The first Zagreb index of a graph $G$ is defined as $\sum_{u \in V} d^2(u)$, where $d(u)$ is the degree of vertex $u$ in $G$. Using the P\'{o}lya-Szeg\H{o} inequality, we in this paper present the first Zagreb…