20.500.12556/DiRROS-25715 Invitation to the subpath number 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. graphs subpath number number of subtrees unbranched catacondensed benzenoids true false true Elsevier Inc. Angleški jezik Ni določen © 2025 The Authors Neznano 2026-01-27 15:47:02 2026-06-17 09:51:54 2026-06-18 04:07:42 0000-00-00 00:00:00 2026 0 0 Soavtorji: Jelena Sedlar, Riste Škrekovski, Yu Yang; 11 str. [article no.] 129646 Vol. 509 Jan. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2025-02-27 0000-00-00 2025-07-25 519.17 0096-3003 10.1016/j.amc.2025.129646 259072003 https://www.sciencedirect.com/science/article/pii/S0096300325003728 1 0d3cb518-fb8f-11f0-a15d-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=39041 RAZ_Knor_Martin_2026.pdf RAZ_Knor_Martin_2026.pdf 1 120E3F3232C848A5EC428710AAEF1F84 9ae22cf07e16e0d621daba9c65df920ecb2f7dfd3739bc06619570997388fdb6 1c9e81ae-fb90-11f0-a15d-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=39042 Rudolfovo – Znanstveno in tehnološko središče Novo mesto 0 0 0