Graceful Labeling of some Join Graphs and the Subdivision of Complete Bipartite Graphs

A. Panpa, P. Chaiprasert and C. Tisklang

Journal of Applied Mathematics, 2025, vol. 2025, 1-6

Abstract: The join of graphs G and H, denoted by G+H, is the graph obtained from the disjoint union of G and H by joining each vertex in G to each vertex in H. An edge uw is said to be subdivided if uw is replaced by the path P:uvw, where v is the new vertex. A graph obtained by subdividing each edge of a graph G is called the subdivision of G, and is denoted by SG. In this paper, we present results on the gracefulness of some join graphs, namely, T+Pn, T+Pnm, C4+Op, Psm+Ptn for some m,n,s,t and T is a graceful tree. We also show that the subdivision graph SKm,n of complete bipartite graph Km,n is graceful.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:5533881

DOI: 10.1155/jama/5533881

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