Bipartite Powers of Certain Classes of Bipartite Graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915515189952512 |
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| author | Paul, Indrajit Das, Ashok Kumar |
| author_facet | Paul, Indrajit Das, Ashok Kumar |
| contents | The concept of graph powers has been extensively studied in graph theory. Analogous to graph powers, Chandran et al. [3] introduced the notion of bipartite powers for bipartite graphs. In this paper, we show that the class of interval bigraphs, as well as the class of proper interval bigraphs are closed under the operation of taking bipartite powers. Finally, we define strongly closed property for bipartite graphs under powers and have shown that the class of chordal bipartite graphs is strongly closed under bipartite powers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_17279 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bipartite Powers of Certain Classes of Bipartite Graphs Paul, Indrajit Das, Ashok Kumar Combinatorics Discrete Mathematics 05C12, 05C38, 05C62 The concept of graph powers has been extensively studied in graph theory. Analogous to graph powers, Chandran et al. [3] introduced the notion of bipartite powers for bipartite graphs. In this paper, we show that the class of interval bigraphs, as well as the class of proper interval bigraphs are closed under the operation of taking bipartite powers. Finally, we define strongly closed property for bipartite graphs under powers and have shown that the class of chordal bipartite graphs is strongly closed under bipartite powers. |
| title | Bipartite Powers of Certain Classes of Bipartite Graphs |
| topic | Combinatorics Discrete Mathematics 05C12, 05C38, 05C62 |
| url | https://arxiv.org/abs/2404.17279 |