24 Results Found

Circulant networks are a very important and widely studied class of graphs due to their interesting and diverse applications in networking, facility location problems, and their symmetric properties. The structure of the graph ensures that it is symm...

In this work, we study the degree-based topological invariants, and the general sum-connectivity, $AB{C}_4$ , $G{A}_5$ , general Zagreb, $GA$ , generalized Randić, and $ABC$ indices of the line graphs of some rooted product...

Let ${\mathbb{T}}_4=\{\pm 1,\pm i\}$ be the subgroup of fourth roots of unity inside $\mathbb{T}$ , the multiplicative group of complex units. For a ${\mathbb{T}}_4$ -gain graph $\mathsf{\Phi }=(\mathsf{\Gamma },{\mathbb{T}}_4,\phi )$ , we introduce gain function...

The complexity (number of spanning trees) in a finite graph $\Gamma$ (network) is crucial. The quantity of spanning trees is a fundamental indicator for assessing the dependability of a network. The best and most dependable network is the one with the...

Mesh subdivision is a common mesh-processing algorithm used to improve model accuracy and surface smoothness. Its classical scheme adopts a fixed linear vertex update strategy and is implemented iteratively, which often results in excessive mesh smoo...

In this paper, we introduce a new graph operation called subdivision vertex-edge join (denoted by $G_1^S▹(G_2^V\cup G_3^E)$ for short), and then the adjacency spectrum, the Laplacian spectrum and the signless Laplacian spectrum of...

In the studies of quantitative structure–activity relationships (QSARs) and quantitative structure–property relationships (QSPRs), graph invariants are used to estimate the biological activities and properties of chemical compounds. In th...

The locating-chromatic number of a graph combines two graph concepts, namely coloring vertices and partition dimension of a graph. The locating-chromatic number is the smallest k such that G has a locating k-coloring, denoted by ${\chi }_L\left(G\right)$. This article p...

A topological index is a number related to the atomic index that allows quantitative structure–action/property/toxicity connections. All the more vital topological indices correspond to certain physico-concoction properties like breaking point,...

Entropy is essential. Entropy is a measure of a system’s molecular disorder or unpredictability, since work is produced by organized molecular motion. Entropy theory offers a profound understanding of the direction of spontaneous change for man...

In order to increase the paired-domination number of a graph G, the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number ${\mathrm{sd}}_{{\gamma }_{pr}}\left(G\right)$ of G. It is wel...

In this paper, motivated by the recently introduced topological indices—the Sombor index, Sombor coindex, and Lanzhou index, we define a new index—the Lanzhou coindex of a graph. Furthermore, we investigate the Sombor index (coindex) and...

In the modern era, mathematical modeling consisting of graph theoretic parameters or invariants applied to solve the problems existing in various disciplines of physical sciences like computer sciences, physics, and chemistry. Topological indices (TI...

A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties. Miličević reformulated the original Zagreb indices...

Topological indices are numerical values associated with a graph (structure) that can predict many physical, chemical, and pharmacological properties of organic molecules and chemical compounds. The distance degree ( $DD$ ) index was introduced...

A map on a closed surface is a two-cell embedding of a finite connected graph. Maps on surfaces are conveniently described by certain trivalent graphs, known as flag graphs. Flag graphs themselves may be considered as maps embedded in the same surfac...

An irregularity index $IR\left(\mathsf{\Gamma }\right)$ of a graph $\mathsf{\Gamma }$ is a nonnegative numeric quantity (i.e., $IR\left(\mathsf{\Gamma }\right)\ge 0$) such that $IR\left(\mathsf{\Gamma }\right)=0$ iff $\mathsf{\Gamma }$ is a regular graph. In this paper, we show that $IRC$ closely correlates with the normal boiling point $T_{}$...

Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-w...

A graph operator is a mapping $F:\mathsf{\Gamma }\to {\mathsf{\Gamma }}^{\prime }$ , where $\mathsf{\Gamma }$ and ${\mathsf{\Gamma }}^{\prime }$ are families of graphs. The different kinds of graph operators are an important topic in Discrete Mathematics and its applicat...

For a graph G with no isolated vertex, let ${\gamma }_{pr}\left(G\right)$ and ${\mathrm{sd}}_{{\gamma }_{pr}}\left(G\right)$ denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order $n\ge 4$ different from a healthy spider...

The space-mapping method provides a novel method for dimension formulae explanation and basis construction for the spline space over hierarchical T-meshes. By the space-mapping method, we provide a unique basis construction framework that incorporate...

A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number γ_pr(G) of G. Th...

The precise application of tightening torque is one of the important measures to ensure accurate bolt connection and improvement in product assembly quality. Currently, due to the limited assembly space and efficiency, a wrench without the function o...

The Hengduan Mountains region (HMR) is vulnerable to flash flood disasters, which account for the largest proportion of flood-related fatalities in China. Flash flood regionalization, which divides a region into homogeneous subdivisions based on flas...