相关论文: Edge Resolvability of Crystal Cubic Carbon Structu…
A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a "viewing graph". Whether or not these fundamental matrices are generically sufficient to recover the global camera configuration…
In chemical graph theory, topological indices are widely used as numerical descriptors for establishing quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR). These indices…
For a graph $\mathbb{Q}=(\mathbb{V},\mathbb{E})$, the transformation graphs are defined as graphs with vertex set being $\mathbb{V(Q)} \cup \mathbb{E(Q)}$ and edge set is described following certain conditions. In comparison to the…
The atom-bond connectivity (ABC) index is a degree-based molecular structure descriptor that can be used for modelling thermodynamic properties of organic chemical compounds. Motivated by its applicable potential, a series of investigations…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
The structure of the character degree graphs $\Delta(G)$, i.e. the prime graphs on the set $\mathrm{cd}(G)$ of the irreducible character degrees of a finite group $G$, such that $G$ is solvable and $\Delta(G)$ has diameter three, remains an…
The energy of arbitrary graphene edge is derived in analytical form. It contains a "chemical phase shift", determined by the chemical conditions at the edge. Direct atomistic computations support the universal nature of the relationship.…
The non-solvable graph of a finite group G is a simple graph whose vertices are the elements of G and there is an edge between x and y if and only if the subgroup generated by x and y is not solvable. The isolated vertices in the…
The task of identifying resolving sets has been extensively studied due to its wide relevance in fields such as chemistry, robot navigation, combinatorial optimization, pattern recognition, and image processing. These applications have…
Crystal morphologies are important for the design and functionality of devices based on low-dimensional nanomaterials. The equilibrium crystal shape (ECS) is a key quantity in this context. It is determined by surface energies, which are…
Let $G$ be a finite solvable group and let $\Delta(G)$ be the character degree graph of $G$. In this paper, we obtain the metric dimension of certain character degree graphs. Specifically, we calculate the metric dimension for a regular…
Let $G$ be a finite group. The solubility graph associated with the finite group $G$, denoted by $\Gamma_{\cal S}(G)$, is a simple graph whose vertices are the non-trivial elements of $G$, and there is an edge between two distinct elements…
Given a finite group $G$, the character graph, denoted by $\Delta(G)$, for its irreducible character degrees is a graph with vertex set $\rho(G)$ which is the set of prime numbers that divide the irreducible character degrees of $G$, and…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
An equitable coloring of a graph $G=(V,E)$ is a (proper) vertex-coloring of $G$, such that the sizes of any two color classes differ by at most one. In this paper, we consider the equitable coloring problem in block graphs. Recall that the…
Theoretical study of graphite (graphene) edge is done. The most stable edge orientation is calculated to be a zigzag [110] edge. Possible applications of the result to the formation of different graphitic structures are discussed.
The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected…
Graph-structured data arise in a variety of real-world context ranging from sensor and transportation to biological and social networks. As a ubiquitous tool to process graph-structured data, spectral graph filters have been used to solve…
The atomic structure of graphene edges is critical in determining the electrical, magnetic, and chemical properties of truncated graphene structures, notably nanoribbons. Unfortunately, graphene edges are typically far from ideal and suffer…
We consider the following natural graph cut problem called Critical Node Cut (CNC): Given a graph $G$ on $n$ vertices, and two positive integers $k$ and $x$, determine whether $G$ has a set of $k$ vertices whose removal leaves $G$ with at…