Extremal graphs of diameter 3

Abstract

AbstractThis paper is concerned with graphs of order n and diameter at most 3 having the property that by deleting any s or fewer vertices (edges) the resulting subgraphs (partial graphs) have duameter at most. λ. A graph satisfying the above constraints and having minimum number of edges is said to be extramal. A characterization of extremal graphs is presented for the case s = 1.Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 35.