2024/10/10 by Gao, Jing, Li, Xueliang
#05C35 #05C50 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2410.07721
A graph G is said to be F-free if it does not contain F as a subgraph. A theta graph, say θl1,l2,l3, is the graph obtained by connecting two distinct vertices with three internally disjoint paths of length l1, l2, l3, where l1≤ l2≤ l3 and l2≥2. Recently, Li, Zhao and Zou [arXiv:2409.15918v1] characterized the θ1,p,q-free graph of size m having the largest spectral radius, where q≥ p≥3 and p+q≥2k+1≥7, and proposed a problem on characterizing the graphs with the maximum spectral radius among θ1,3,3-free graphs. In this paper, we consider this problem and determine the maximum spectral radius of θ1,3,3-free graphs with size m and characterize the extremal graph. Up to now, all the graphs in G(m,θ1,p,q) which have the largest spectral radius have been determined, where q≥ p≥ 2.