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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Open Access Research Article

Advanced computational methods for compact mean labeling in star graphs

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pp. 2289–2297Vol. 29Issue 6June 2026DOI: 10.47974/JDMSC-2570 Crossmark XML
Received:
01 May 2025
Published Online:
20 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2570
Pages:
2289–2297

Abstract

Graph labeling involves assigning unique integer values to the vertices and edges of a graph, starting from zero or a higher value. A star graph, denoted as K(1, r), consists of a central vertex connected to r peripheral vertices, forming a complete bipartite graph. In this research, the notion of compact mean labeling using star graphs is explored. Typically, a star graph has p < q edges. However, for compact mean labeling, the graph should have p ≤ q. To resolve this inconsistency, the vertex labeling of the graph has been determined from zero to 3q-p. This proposed extended compact mean labeling technique is verified for the bi-star graphs, the join sum of the star graph, and the union of the star graph. Our findings offer new insights into the characteristics and application of star graphs in extended compact mean labeling, particularly in comparing the strong and weak ties within a network.

Keywords

Subject Classifications

05C78

References

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