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On antipodal, eccentric and super-eccentric graph of a graph. (English) Zbl 0688.05041

Summary: A graph J(G) is said to be super-eccentric graph of a graph G if \(V(G)=V(J(G))\) and uv\(\in E(J(G))\) whenever d(u,v)\(\geq r\), where r is the radius of the graph G. In this paper the concept of super-eccentric graphs of a graph is introduced and also the results relating to antipodal, eccentric and super-eccentric graphs of a graph are presented with the characterizations of antipodal, eccentric and super-eccentric geodetic graphs. Also some graph equations connecting antipodal, eccentric and super-eccentric graphs are discussed.

MSC:

05C35 Extremal problems in graph theory
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