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Strongly indexable graphs

✍ Scribed by B.D. Acharya; S.M. Hegde

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 633 KB
Volume: 93
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90248-z

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✦ Synopsis

Acharya, B.D. and S.M. Hegde, Strongly indexable graphs, Discrete Mathematics 93 (1991) 123-129. A (p, q)-graph G = (V, E) is said to be strongly k-indexable if it admits a strong k-indexer viz., an injective function f : V -{C, 1, 2, . . . , p -1) such that f(x)+f(y)=f+(xy)Ef+(E)={k,k+l,k+2,..

. , k+q-1).

In the terms defined here, k will be omitted if it happens to be unity. We find that a strongly indexable graph has exactly one nontrivial component which is either a star or has a traingle. In any strongly k-indexable graph the minimum point degree is at most 3. Using this fact we show that there are exactly three strongly indexable regular graphs, viz. &, K, and K, X K,. If an eulerian (p, q)-graph is strongly indexable then 9 = 0, 3 (mod 4).

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