20.500.12556/RUL-170844 On the fractional matching extendability of Cayley graphs of abelian groups Fractional matching extendability is a concept that brings together two widely studied topics in graph theory, namely that of fractional matchings and that of matching extendability. A fractional matching of a graph Γ with edge set E is a function f from E to the real interval [0,1] with the property that for each vertex v of Γ, the sum of f-values of all the edges incident to v is at most 1. When this sum equals 1 for each vertex v, the fractional matching is perfect. A graph of order at least 2t+1 is fractional t-extendable if it contains a matching of size t and if each such matching M can be extended to a fractional perfect matching in the sense that the corresponding function f assigns value 1 to each edge of M. In this paper, we study fractional matching extendability of Cayley graphs of Abelian groups. We show that, except for the odd cycles, all connected Cayley graphs of Abelian groups are fractional 1-extendable and we classify the fractional 2-extendable Cayley graphs of Abelian groups. This extends the classification of 2-extendable (in the classical sense) connected Cayley graphs of Abelian groups of even order from 1995, obtained by Chan, Chen and Yu. fractional matching extendability Cayley graph abelian groups Abelove skupine Cayleyjev graf true false true Angleški jezik Slovenski jezik Članek v reviji 2025-07-18 07:44:27 2025-07-18 07:44:27 2025-07-21 16:05:17 0000-00-00 00:00:00 2025 0 0 22 str. iss. 3, art. P3.9 Vol. 32 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 1077-8926 10.37236/13360 242972931 RAZ_Kuzman_Bostjan_2025.pdf RAZ_Kuzman_Bostjan_2025.pdf 1 0408E385B89EB8FDBF2E3A953ACA8A63 8bfb74455b114faf7f74037024abe203cf1e84235651708ebd2becfb0e8e4fb7 ee55452f-639a-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=213108 https://www.combinatorics.org/ojs/index.php/eljc/article/view/v32i3p9 1 4715dabd-639a-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=213103 Pedagoška fakulteta 0 0 0