相关论文: Diminished Sombor index and its relationship with …
Topological indices are molecular descriptors that describe the properties of chemical compounds. These topological indices correlate specific physico-chemical properties like boiling point, enthalpy of vaporization, strain energy, and…
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 sigma index of a graph, defined as the population variance of its degree sequence, is a fundamental measure of structural irregularity. In this paper, we introduce and systematically investigate its natural extension to fuzzy graphs,…
The distance sensitivity oracle (DSO) problem asks us to preprocess a given graph $G=(V,E)$ in order to answer queries of the form $d(x,y,e)$, which denotes the shortest path distance in $G$ from vertex $x$ to vertex $y$ when edge $e$ is…
Topological indices play a significant role in mathematical chemistry. Given a graph $\mathcal{G}$ with vertex set $\mathcal{V}=\{1,2,\dots,n\}$ and edge set $\mathcal{E}$, let $d_i$ be the degree of node $i$. The degree-based topological…
The domatic number of a graph $G$ is the maximum number of pairwise disjoint dominating sets of $G$. We are interested in the LP-relaxation of this parameter, which is called the fractional domatic number of $G$. We study its extremal value…
Given an integer $k\ge1$, an edge-$k$-coloring of a graph $G$ is an assignment of $k$ colors $1,\ldots,k$ to the edges of $G$ such that no two adjacent edges receive the same color. A vertex-distinguishing (resp. sum-distinguishing)…
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
The harmonic index of a graph $G$ is defined as the sum of weights $\frac{2}{deg(v) + deg(u)}$ of all edges $uv$ of $E (G)$, where $deg (v)$ denotes the degree of a vertex $v$ in $V (G)$. In this note we generalize results of [L. Zhong, The…
The distinguishing index $D'(G)$ of a graph $G$ is the least number of colors necessary to obtain an edge coloring of $G$ that is preserved only by the trivial automorphism. We show that if $G$ is a connected $\alpha$-regular graph for some…
Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have…
An independent dominating set D of a graph G = (V,E) is a subset of vertices such that every vertex in V \ D has at least one neighbor in D and D is an independent set, i.e. no two vertices of D are adjacent in G. Finding a minimum…
Topological relations between three degree-based invariants of a connected graph G are investigated. We present novel inequalities including M1(G), M2(G) and F(G), and show that in all cases equality holds if G is a regular or a semiregular…
The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has a vertex (edge) labeling with $d$ labels that is preserved only by a trivial automorphism. In this paper we consider the maximal…
The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the first variable Zagreb index $M_1^\alpha$, and to characterize the set of extremal graphs with respect to them. Our main…
For an oriented link diagram D, the warping degree d(D) is the smallest number of crossing changes which are needed to obtain a monotone diagram from D. We show that d(D)+d(-D)+sr(D) is less than or equal to the crossing number of D, where…
A set $D \subseteq V$ for the graph $G=(V, E)$ is called a dominating set if any vertex $v\in V\setminus D$ has at least one neighbor in $D$. Fomin et al.[9] gave an algorithm for enumerating all minimal dominating sets with $n$ vertices in…
The study of graphs associated with of various algebraic structures is an emerging topic in algebraic graph theory. Recently, the concept of nonzero component graph of a finite dimensional vector space $\Gamma(\mathbb{V})$ was put forward…
The weakly zero-divisor graph $W\Gamma(R)$ of a commutative ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$ and two distinct vertices $x$, $y$ are adjacent if and only if there exist $w\in {\rm…
The forgotten topological index or F-index of a graph is defined as the sum of degree cube of all the vertices of the graph. This index was introduced by Gutman and Trinajesti\'{c} more than 40 years ago. In this paper, we derive F-index of…