T-Odd Sequential Harmonious Labeling of Cycle CN with Parallel Chords
A. Uma Maheswari1, V. Srividya2
1A. Uma Maheswari, Department of Mathematics, Quaid-e-Millath Government College for Women, Chennai (Tamil Nadu), India.
2V. Srividya, Department of Mathematics, Bharathi women’s College, Chennai (Tamil Nadu), India.
Manuscript received on 18 June 2019 | Revised Manuscript received on 25 June 2019 | Manuscript published on 30 June 2019 | PP: 2184-2188 | Volume-8 Issue-5, June 2019 | Retrieval Number: E7357068519/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Labeling is an active area of research in graph theory with its applications in communication network, coding theory, channel assignment problems and data base management. Graceful Labeling, Harmonious Labeling and variations of these Labelings are the majorlabeling methodologies used in the theory of graphs. Some odd harmonious graphs are paths, cyclesC4n, caterpillars, shadow graph of a path and a star. Odd sequential harmonious labeling of trees, double quadrilateral snakes,twigs and middle graph of a path have been established.In this paper, a generalisation of odd sequential harmonious labeling on cycle related graphs was considered and shown that cycles Cn with parallel chords and new families of graphs based on cycles Cn with parallel chords are t-odd sequential harmonious for all positive integers t ≥ 1 with suitable illustrations.
Keywords: Cycles With Parallel Chords, Chain, Harmonious Labeling, Path Union, T-Odd Sequential Harmonious Labeling. Subject Classification: 05C78
Scope of the Article: Classification