On Eccentric Sets of Edges in Graphs

Masakazu SENGOKU
Takeo ABE

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E74-A    No.4    pp.687-691
Publication Date: 1991/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Issue on Discrete Mathematics and Its Applications)

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We introduce the distance between two edges in a graph (nondirected graph) as the minimum number of edges in a tieset with the two edges. Using the distance between edges we define the eccentricity ετ (ej) of an edge ej. A finite nonempty set J of positive integers (no repetitions) is an eccentric set if there exists a graph G with edge set E such that ετ (ej) J for all ei E and each positive integer in J is ετ (ej) for some ej E. In this paper, we give necessary and sufficient conditions for a set J to be eccentric.