• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology

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Indian Journal of Science and Technology

Year: 2023, Volume: 16, Issue: 44, Pages: 4038-4047

Original Article

Arithmetic Sequential Graceful Labeling of Star Related Graphs – II

Received Date:12 August 2023, Accepted Date:09 October 2023, Published Date:26 November 2023

Abstract

Objectives: To identify a new family of arithmetic sequential graceful graphs. Methods : The methodology involves mathematical formulation for labeling of the vertices of a given graph and subsequently establishing that these formulations give rise to arithmetic sequential graceful labeling. Findings: Here, we introduce the square graph , which shares its vertex set with G. In , two vertices are considered adjacent if their distance in is either 1 or 2. To further elucidate, we identify the splitting graph as an extension of G. Specifically, for each vertex in G, we introduce a corresponding new vertex . Additionally, we demonstrate the construction of the W-star graph. This graph is formed by connecting the apex vertex of the 1st star graph to the apex vertex of the 2nd star graph through a path of length 3. Subsequently, we connect the apex vertex of the 2nd star graph to the apex vertex of the 3rd star graph, also via a path of length 3. Novelty: Here we give arithmetic sequential graceful labeling to a new family of graphs, namely W-star, Square of graph G, splitting graph, Banana tree and proved that these graphs possess arithmetic sequential graceful labeling.

Keywords: Star graph, W­star, Square of graph G, Splitting graph, Banana tree, Graceful labeling

References

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Copyright

© 2023 Sumathi & Geetha Ramani. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)

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