Related papers: On certain topological indices of graphs
The vertex $k$-partiteness $v_k(G)$ of graph $G$ is defined as the fewest number of vertices whose deletion from $G$ yields a $k$-partite graph. In this paper, we introduce two concepts: monotonic decreasing topological index and monotonic…
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…
We consider topological indices I that are sums of f(deg(u)) f(deg(v)), where {u,v} are adjacent vertices and f is a function. The Randi{\'c} connectivity index or the Zagreb group index are examples for indices of this kind. In earlier…
Let $I(G)$ be a topological index of a graph. If $I(G+e)<I(G)$ (or $I(G+e)>I(G)$, respectively) for each edge $e\not\in G$, then $I(G)$ is monotonically decreasing (or increasing, respectively) with the addition of edges. In this article,…
The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced to study the structure-dependency of total…
In the last forty years, many scientists used graph theory to develop mathematical models for analyzing structures and properties of various chemical compounds. In this paper, we will establish formulas and bounds for generalized first…
Very recently, the first geometric-arithmetic index $GA$ and arithmetic-geometric index $AG$ were introduced in mathematical chemistry. In the present paper, we first obtain some lower and upper bounds on $AG$ and characterize the extremal…
The topological indices $irr(G)$ related to the \emph{first Zagreb index,} $M_1(G)$ and the \emph{second Zagreb index,} $M_2(G)$ are the oldest irregularity measures researched. Alberton $[3]$ introduced the \emph{irregularity} of $G$ as…
Topological indices are real numbers invariant under graph isomorphisms. Chromatic analogue of topological indices has been introduced recently in literature in 2017. Mainly, chromatic versions of Zagreb indices are studied lately. This…
In this paper, we refer to a asymptotic degree sequence as $\mathscr{D}=(d_1,d_2,\dots,d_n)$. The examination of topological indices on trees gives us a general overview through bounds to find the maximum and minimum bounds which reflect…
In this work we obtain new lower and upper optimal bounds of general Sombor indices. Specifically, we have inequalities for these indices relating them with other indices: the first Zagreb index, the forgotten index and the first variable…
In this paper, we study the higher Steklov eigenvalues of graphs on surfaces. We obtain the upper bound of higher Steklov eigenvalues of a finite graph $G$ with boundary $B$ and genus $g$ by using metrical deformation via probability flows.…
In this paper, we examine a specific type of random chains and propose an unified approach to studying the degree-based topological indices, including their extreme values. We derive explicit analytical expressions for the expected values…
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 $\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 first multiplicative Zagreb index of a graph $G$ is the product of the square of every vertex degree, while the second multiplicative Zagreb index is the product of the degree of each edge over all edges. In our work, we explore the…
In this paper, we provide the irregularity properties of trees with strong support vertex by analyzing two prominent topological indices: the Albertson index and the Sigma index. We further establish extremal bounds for both indices across…
In this paper we introduce a variation of the well-known Zagreb indices by considering a proper vertex colouring of a graph $G$. The chromatic Zagreb indices are defined in terms of the parameter $c(v), v \in V(G)$ instead of the invariant…
We present lower and upper bounds for the geometric-arithmetic index of unicyclic graphs and provide extremal graphs for the corresponding bounds.
For a simple graph $G$ with $n$ vertices and $m$ edges, the first Zagreb index and the second Zagreb index are defined as $M_1(G)=\sum_{v\in V}d(v)^2 $ and $M_2(G)=\sum_{uv\in E}d(u)d(v)$. In \cite{VGFAD}, it was shown that if a connected…