Abstract
Most graph labeling methods trace their origion to one introduced by Rosa [1] called such a labeling a β-valuation and Golomb [2] subsequently called graceful labeling, and one introduced by Graham and Sloane [3] called harmonious labeling. Several infinite families of graceful and harmonious graphs have been reported. Many illustrious works on graceful graphs brought a tide to different ways of labeling the elements of graph such as odd graceful.
Highlights
Graph labeling is an active area of research in graph theory which has mainly evolved through its many applications in coding theory, communication networks, mobile telecommunication system
[8] Liang and Bai have shown that the kC4 − snake graph is an odd harmonious graph for each k ≥ 1
We show that the kC4 − snake with m-pendant edges for each k, m ≥ 1
Summary
Graph labeling is an active area of research in graph theory which has mainly evolved through its many applications in coding theory, communication networks, mobile telecommunication system. Any graph G = kCn − snake, can be represented by a string. Gracefulness of the kind of kC4 − snake studied by Gnanajothi have string 1, 1,..., 1. We obtain in Theorem 2.4 an odd harmonious labelings of the kC4 − snake with string 1,1,...,1. We obtain an odd harmonious labeling of kCn − snake with the sequence string is 1, 1,..., 1 and when n ≡ 0 (mod 4). We prove that the all subdivision of 2 m ∆k snake are odd harmonious for each k, m ≥ 1
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