| Title: | Invitation to the subpath number |
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| Authors: | ID Knor, Martin (Author)
ID Sedlar, Jelena (Author)
ID Škrekovski, Riste (Author)
ID Yang, Yu (Author) |
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| Files: |  URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0096300325003728
 PDF - Presentation file, download (1,26 MB)
MD5: 120E3F3232C848A5EC428710AAEF1F84
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  RUDOLFOVO - Rudolfovo - Science and Technology Centre Novo Mesto
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| Abstract: | In this paper we count all the subpaths of a given graph ▫$G$▫, including the subpaths of length zero, and we call this quantity the subpath number of ▫$G$▫. The subpath number is related to the extensively studied number of subtrees, as it can be considered as counting subtrees with the additional requirement of maximum degree being two. We first give the explicit formula for the subpath number of trees and unicyclic graphs. We show that among connected graphs on the same number of vertices, the minimum of the subpath number is attained for any tree and the maximum for the complete graph. Further, we show that the complete bipartite graph with partite sets of almost equal size maximizes the subpath number among all bipartite graphs. The explicit formula for cycle chains, i.e. graphs in which two consecutive cycles share a single edge, is also given. This family of graphs includes the unbranched catacondensed benzenoids which implies a possible application of the result in chemistry. The paper is concluded with several directions for possible further research where several conjectures are provided. |
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| Keywords: | graphs, subpath number, number of subtrees, unbranched catacondensed benzenoids |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 27.02.2025 |
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| Publication date: | 25.07.2025 |
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| Publisher: | Elsevier Inc. |
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| Year of publishing: | 2026 |
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| Number of pages: | 11 str. |
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| Numbering: | Vol. 509, [article no.] 129646 |
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| PID: | 20.500.12556/DiRROS-25715  |
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| UDC: | 519.17 |
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| ISSN on article: | 0096-3003 |
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| DOI: | 10.1016/j.amc.2025.129646 |
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| COBISS.SI-ID: | 259072003 |
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| Copyright: | © 2025 The Authors |
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| Note: | Soavtorji: Jelena Sedlar, Riste Škrekovski, Yu Yang;
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| Publication date in DiRROS: | 17.06.2026 |
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| Views: | 60 |
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| Downloads: | 39 |
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| Metadata: |    |
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