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Abstract

The locating-chromatic number of a graph combines proper vertex coloring with vertex identification through distances to color classes. Although this parameter has been studied for many graph families, general results for bipartite graphs remain limited. Bipartite graphs contain structural symmetries, especially within each partite set, making it difficult to obtain distinct color codes. This paper establishes lower and upper bounds for the locating-chromatic number of bipartite graphs using neighborhood equivalence classes in the two partite sets. The bounds describe the effect of identical neighborhoods on the number of distinguishable color codes. They are shown to be tight, and regular complete bipartite graphs are identified as extremal examples. The paper also considers corona products of regular complete bipartite graphs and complements of complete graphs, for which bipartiteness is preserved. Exact values of the locating-chromatic number are obtained for all relevant numbers of attached vertices, indicating how the number and arrangement of pendant vertices affect the coloring process. These results provide a basis for studying locating colorings in bipartite and corona graphs and complement existing results in the literature.

Keywords

Bipartite graph, Color code, Complete graph, Corona product, Locating-chromatic number

Subject Area

Mathematics

Article Type

Article

First Page

2891

Last Page

2899

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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