The central ratio of a graph

✍ Scribed by Fred Buckley

• Book ID: 103057668
• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 419 KB
• Volume: 38
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(82)90164-9

✦ Synopsis

We examine several graph equations involving the center, C(G), af a graph G. The central ratio of G, denoted c(G), is the ratio of jCCG,j to IV(G)(. We show that for any rat%?1 number r. where 0~ r s 1. there is a graph G with c(G) = r. For all such r, we describe a corresponding minimal graph. Graphs for which c(G) = 1 a,< calletl self-centered. We give the range of values for IE(G)I for self-centered connected graph,; on M vertices. We then aracterize all trees whose center vertices get interchanged undc r zomp'ementatiop.