相关论文: Chromatic Topological Indices of Certain Cycle Rel…
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…
A topological index of a graph $G$ is a real number which is preserved under isomorphism. Extensive studies on certain polynomials related to these topological indices have also been done recently. In a similar way, chromatic versions of…
Topological indices are numerical invariants derived from molecular graphs and play an important role in characterizing chemical compounds and predicting their properties. Among the earliest descriptors are the classical Zagreb indices…
The aim of this paper is to obtain new inequalities for a large family of topological indices restricted to unicyclic graphs and to characterize the set of extremal unicyclic graphs with respect to them. This family includes variable first…
A topological index is a real number which is derived from a network or a graph by mathematically that characterizes the whole of its structural properties. Recently, there are various topological indices that have been introduced in…
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…
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…
Motivated by the recently introduced topological index, the Somber index, we define a new topological index of a graph in this paper, we call it Sombor coindex. The Sombor coindex is defined by considering analogous contributions from the…
Graph theory has provided a very useful tool, called topological indices which are a number obtained from the graph $G$ with the property that every graph $H$ isomorphic to $G$, value of a topological index must be same for both $G$ and…
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…
By a finite type-graph we mean a graph whose set of vertices is the set of all $k$-subsets of $[n]=\{1,2,\ldots, n\}$ for some integers $n\ge k\ge 1$, and in which two such sets are adjacent if and only if they realise a certain order type…
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…
Making use of a majorization technique for a suitable class of graphs, we derive upper and lower bounds for some topological indices depending on the degree sequence over all vertices, namely the first general Zagreb index and the first…
For a colour cluster $\mathbb{C} =(\mathcal{C}_1,\mathcal{C}_2, \mathcal{C}_3,\ldots,\mathcal{C}_\ell)$, where $\mathcal{C}_i$ is a colour class such that $|\mathcal{C}_i|=r_i$, a positive integer, we investigate two types of simple…
Topological indices are graph invariants numeric quantities, which are utilized by researchers to analyze a variety of physiochemical aspects of molecules. The goal of developing topological indices is to give each chemical structure a…
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…
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…
Graph operations are crucial for building complicated network architectures from simple graphs. In [7], authors defined two new variants of Corona product and investigated some topological indices. In this paper, we extended the work and…
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…