Jun 2026· Journal of Physics, Conference Series· Vol 3268, pp. 012005· 0 citations· 18 references
Physics
Abstract
Let G be a finite group. We introduce a new graph definition, called the pseudo A4-graph, as an extension of the classical A4-graph. The pseudo A4-graph of G or PA4-graph is a simple graph ΓG whose vertices are elements of G, and two distinct vertices a and b are joined by an edge if and only if ab−1 = ba−1. This paper presents the formulas for certain graph invariants such as the number of edges, diameter, total degree, chromatic number, clique number, independence number, domination number, matching number, and graph energy. The method involves constructing the A4-graphs of dihedral groups, analyzing their structure, and systematically computing graph invariants through algebraic reasoning and combinatorial techniques to establish fundamental properties and relationships. One of the results in this paper comply with the well-known fact that the energy of a graph is always an even integer.
Akbari, Elphick, Kumar, Pragada and Tang [Discrete Math. 349 (2026) 114953] conjectured that for every connected graph G, the line graph of G has at most one more positive than negative adjacency eigenvalue; equivalently, the signature of a connected line graph is at most 1. We refute the conjecture with two independen...
Sharma and Panda recently proved that every bipartite graph with a perfect matching has property (P); that is, it admits a non-singular real symmetric matrix with support graph G for which every vertex is a P -vertex. In this paper, we extend their result from bipartite graphs to arbitrary graphs. To this end, we intro...
A graph category is a category with a set of graphs or similar structures (such as, directed graphs, signed graphs, etc.) playing the role of objects, and an appropriate notion of homomorphism playing the role of morphisms. The characterization of multiplicative objects are important open problems in categories of undi...
S. Das, Moritz Muhlenthaler, Sagnik Sen et al.· arXiv.org· 0 citations
In this paper, we construct a class of infinite graphs, called substitution graphs. The vertex set consists of all finite words over a finite alphabet. A directed graph is formed by adding vertical edges connecting each word to its children and horizontal edges defined recursively by two finite directed graphs G and J:...
Qing-Cheng Zeng, Cheng Zeng, Yu-Mei Xue et al.· 0 citations
We prove that a graph $G$ is quasi-planar - i.e. quasi-isometric to a planar graph - if and only if it can be obtained by iterating the following two operations a bounded number of times: a) subdividing each edge into a path of bounded length, and b) taking the intersection graph of a family of connected subgraphs cove...
For a graph and a graph family , let denote the maximum number of copies of in an ‐free ‐vertex graph. Let . Bai, Tompkins, and Well conjectured that is attained if and each block of the graph is a . In this paper, we determine the exact value of and the extremal graphs for all . The novelty of our proof is to give a...
Xiaojun Zhao, Yuejian Peng· Journal of Graph Theory· 2 citations
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