Some Minimal Graphs by Interlacing Eigenvalues

✍ Scribed by H.B. Walikar; P.R. Hamipholi; H.S. Ramane

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 159 KB
• Volume: 15
• Category: Article
• ISSN: 1571-0653
• DOI: 10.1016/s1571-0653(04)00587-6

✦ Synopsis

Let (G) be a simple graph with (p) vertices and let (A(G)) be the adjacency matrix of (G). The characteristic polynomial of (G) is the characteristic polynomial of (A(G)) and roots of the characteristic equation are the eigenvalues of (G). In this paper we compute the characteristic polynomial of a class of graphs and show that the same class of graphs are minimal. (Here minimal indicates graphs with diameter (d) and exactly (d+1) different eigenvalues).