Related papers: On Topological Indices in Trees: Fibonacci Degree …
In this paper, we presented a study of topological indices on trees, where we show a relationship with irregularity of Albertson index and minimum, maximum degrees $\delta,\Delta$ of graph $G$, where contribute vital roles in determining…
In this paper, we investigate The relationship between the Albertson index and the first Zagreb index for trees. For a tree $T=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges, we provide several bounds and exact formulas for these two…
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…
This study explores the irregularity properties of trees with prescribed degree sequences by analyzing two prominent topological indices: the Albertson index and the sigma index. With a particular emphasis on caterpillar trees -frequently…
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 presents novel and sharp bounds on the Albertson index of trees, revealing deep connections between degree sequences and graph irregularity where the Albertson index of Caterpillar tree satisfy \[…
We establish sharp extremal bounds on the Albertson and Sigma irregularity indices for trees with prescribed degree sequences, with emphasis on caterpillar trees as key extremal configurations. New lower and upper bounds are derived in…
In this paper, degree-based topological indices play a key role in the structural analysis of graphs in this paper and have significant uses in chemical graph theory. We investigate the connections between three such tree indices: the…
In this paper, the study of extreme value bounds for topological indices is crucial for understanding their influence on trees and bipartite graphs. For integers $\alpha, p$ satisfying $1 \leq p \leq \alpha \leq \Delta - 3$, the minimum…
In this paper, topological indices play a significant role in the analysis of caterpillar trees, especially due to their applications in chemical graph theory. We presented a study on topological indices related to the Sigma index, which we…
In this paper, we establishe the extremal bounds of the topological indices -- Sigma index -- focusing on analyzing the sharp upper bounds and the lower bounds of the Sigma index, which is known $\sigma(G)=\sum_{uv\in…
In this paper, the investigates Adriatic indices, specifically the sum lordeg index where it defined as $SL(G) = \sum_{u \in V(G)} \deg_G(u) \sqrt{\ln \deg_G(u)}$ and the variable sum exdeg index $SEI_a(G)$ for $a>0$, $a\neq 1$. We present…
This paper introduces the concept of the Fibonacci Word Index $\operatorname{FWI}$, a novel topological index derived from the Albertson index, applied to trees constructed from Fibonacci words. Building upon the classical Fibonacci…
A topological index reflects the physical, chemical and structural properties of a molecule, and its study has an important role in molecular topology, chemical graph theory and mathematical chemistry. It is a natural problem to…
The $\sigma$-irregularity index of a graph is defined as the sum of squared degree differences over all edges and provides a sensitive measure of structural heterogeneity. In this paper, we study the problem of maximizing $\sigma(T)$ among…
The sigma index in graph theory refers to a measure of the degree differences between vertices in a graph. The goal is to determine the graphs that have the maximum sigma index within certain classes of graphs. Abdo, Dimitrov, and Gutman…
The sigma-irregularity index $\sigma(G) = \sum_{uv \in E(G)} (d_G(u) - d_G(v))^2$ measures the total degree imbalance along the edges of a graph. We study extremal problems for $\sigma(T)$ within the class of trees of fixed order $n$ and…
Let $d_G(v)$ be the degree of the vertex $v$ in a graph $G$. The Sombor index of $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, which is a new degree-based topological index introduced by Gutman. Let…
In this paper we give new bounds for a several vertex-based and edge-based topological indices of graphs: Albertson irregularity index, degree variance index, Mostar and the first Zagreb index. Moreover, we give a new upper bound for the…
In 2021, the Sombor index was introduced by Gutman, which is a new degree-based topological molecular descriptors. The Sombor index of a graph $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, where $d_G(v)$ is the…