Indexable and strongly indexable graphs. | [Proceedings of Pakistan Academy of Sciences • 2012]

Author(s):

1. Mohamed Abdel-Azim Seoud: Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt

2. Gamal Mabrouk Abdel-Hamid: Department of Mathematics, Military Technical College, Kobry ElKobba, Cairo, Egypt

3. Mohamed Saied Abdel-Aziz Abo Shady: Department of Mathematics, Military Technical College, Kobry ElKobba, Cairo, Egypt

Abstract:

Let G=(V, E) be an (n,m) graph. G is said to be strongly indexable if there exists a bijection ƒ: V→ {0, 1, 2, … …, n-1}, such that ƒ+ (E)={1,2, …, m}, where ƒ+ (u,v)=ƒ (u) + ƒ (v) for any Edge uv ε E. G is said to be indexable if ƒ+ is injective on E. In this paper we construct classes of indexable graphs, and we give an upper bound for the number of edges of any graph on vertices to be indexable. Also, we determine all indexable graphs of order ≤ 6.

Page(s): 139-144

DOI: DOI not available

Published: Journal: Proceedings of Pakistan Academy of Sciences, Volume: 49, Issue: 2, Year: 2012

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