2025/07/18 by Antony, Cyriac, Antony, Jacob, Jinitha Varughese +3
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2507.13821
openalex publication_date 2025/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Oriented line graph, introduced by Kotani and Sunada (2000), is closely related to Hashimato's non-backtracking matrix (1989). It is known that for regular graphs G, the eigenvalues of the adjacency matrix of the oriented line graph L(G) of G are the reciprocals of the poles of the Ihara zeta function of G. We determine the characteristic polynomial of the z-Hermitian adjacency matrix of L(G) for each z∈ ℂ and d-regular graph G with d≥ 3. Special cases of this matrix include the Hermitian adjacency matrix of L(G) and the adjacency matrix of the underlying undirected graph of L(G). We also exhibit an application to star coloring of graphs.