Year: 2024
Type: article
Abstract: Let G be a finite simple graph and let A(G) be its adjacency matrix. Then, G is singular if A(G) is singular. The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. For positive integers ai≥2, i=1,2,…,6. Insert a1−2, a2−2, a3−2, a4−2, a5−2 and a6−2 vertices in the six edges of the complete graph K4, respectively, then the resulting graph is called the K4 homeomorphic graph, denoted by K(a1,a2,a3,a4,a5,a6). In this paper, we give the necessary and sufficient condition for the singularity of K(a1,a2,a3,a4,a5,a6), and we also show that the probability of a K4 homeomorphic graph K(a1,a2,a3,a4,a5,a6) being a singular graph is equal to 193512.
Source: Axioms
Author: Haicheng Ma
Institution: Guangdong University of Science and Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
Award: 图的线性参数和匹配多项式研究
OpenAlex ID: W4405921562