2023/11/08 by Fuyuan Yang, Qiang Sun, Yang, Fuyuan +3
Computer Science · Mathematics · #05C25 #05C35 #05E15 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2311.04401
openalex publication_date 2023/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let n≥ 1 be an integer and \mathbbFq be a finite field of characteristic p with q elements. In this paper, it is proved that the Wenger graph Wn(q) and linearized Wenger graph Lm(q) are edge-girth-regular (v,k,g,λ)-graphs, and the parameter λ of graphs Wn(q) and Lm(q) is completely determined. Here, an edge-girth-regular graph egr(v,k,g,λ) means a k-regular graph of order v and girth g satisfying that any edge is contained in λ distinct g-cycles. As a direct corollary, we obtain the number of girth cycles of graph Wn(q), and the lower bounds on the generalized Turán numbers ex(n, C6, \mathscrC5) and ex(n, C8, \mathscrC7), where Ck is the cycle of length k and \mathscrCk = \C3, C4, … , Ck\.Moreover, there exist a family of egr(2q3,q,8,(q-1)3(q-2))-graphs for q odd, and the order of graph W2(q) and extremal egr(v,q,8,(q-1)3(q-2))-graph have same asymptotic order for q odd.