Related papers: Sharp Bounds for Generalized Zagreb Indices of Gra…

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…

The authors Mili$\breve{c}$evi$\acute{c}$ et al. introduced the reformulated Zagreb indices, which is a generalization of classical Zagreb indices of chemical graph theory. In the paper, we characterize the extremal properties of the first…

Let $\mathbb{G} = (\mathcal{V}, \mathcal{E})$ be a simple connected graph, where $\mathcal{V}$ and $\mathcal{E}$ denote the vertex and edge sets, respectively. The first Zagreb index is defined as $\mathcal{M}_{1}(\mathbb{G}) = \sum_{v \in…

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…

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…

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randi\'c and the Zagreb indices have been used more considerably than any other topological indices in chemical and…

In this paper, we study the limiting behavior of the generalized Zagreb indices of the classical Erd\H{o}s-R\'{e}nyi (ER) random graph $G(n,p)$, as $n\to\infty$. For any integer $k\ge1$, we first give an expression for the $k$-th order…

In this paper, we will construct formulas and bounds for Neighborhood Degree-based indices of graphs and describe graphs that attain the bounds. Furthermore, we will establish a lower bound for the spectral radius of any graph.

We examine the quantity \[S(G) = \sum_{uv\in E(G)} \min(\text{deg } u, \text{deg } v)\] over sets of graphs with a fixed number of edges. The main result shows the maximum possible value of $S(G)$ is achieved by three different classes of…

Recently, a couple of degree-based topological indices, defined using a geometrical point of view of a graph edge, have attracted significant attention and being extensively investigated. Furtula and Oz [Complementary Topological Indices,…

Let G be a graph with vertex set V (G) and edge set E(G). The first generalized multiplicative Zagreb index of G is M_1(G) and the second multiplicative Zagreb index is M_2(G). The multiplicative Zagreb indices have been the focus of…

The paper discusses the edge hyper-Zagreb index of a graph, which is calculated by replacing vertex degrees with edge degrees. The degree of an edge is determined by adding up the degrees of the end vertices of the edge and subtracting 2.…

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…

The second Zagreb index of a graph G is denoted by $M_2(G)=\sum_{uv\in E(G)}d(u)d(v)$. In this paper, we investigate properties of the extremal graphs with the maximum second Zagreb indices with given graphic sequences, in particular…

Let $G=(V,E)$ be a graph with $n$ vertices and $m$ edges. The hyper Zagreb index of $G$, denoted by $HM(G)$, is defined as $HM(G) =\sum\limits_{uv \in E(G)}\left[d_{G}(u)+d_G(v)\right]^{2}$ where $d_G(v)$ denotes the degree of a vertex $v$…

The Zagreb index of a hypergraph is defined as the sum of the squares of the degrees of its vertices. A connected $k$-uniform hypergraph with $n$ vertices and $m$ edges is called bicyclic if $n=m(k-1)-1$. In this paper, we determine the…

In this article, we investigate the Zagreb index, a kind of graph-based topological index, of several random networks, including a class of networks extended from random recursive trees, plain-oriented recursive trees, and random…

For a graph $G$, the first multiplicative Zagreb index $\prod_1$ is equal to the product of squares of the vertex degrees, and the second multiplicative Zagreb index $\prod_2$ is equal to the product of the products of degrees of pairs of…

The concepts of geometric-arithmetic and harmonic indices were introduced in the area of chemical graph theory recently. They have proven to correlate well with physical and chemical properties of some molecules. The aim of this paper is to…

Let $G$ be a graph with order $n(G)$, size $m(G)$, first Zagreb index $M_1(G)$, and second Zagreb index $M_2(G)$. More than twenty years ago, it was conjectured that $\frac{M_1(G)}{n(G)} \leq \frac{M_2(G)}{m(G)}$. Later, Hansen and…