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On the core of a unicyclic graphLevit, Vadim E. ; Mandrescu, EugenA set ▫$S \subseteq V$▫ is independent in a graph ▫$G = (V, E)$▫ if no two vertices from ▫$S$▫ are adjacent. By core▫$(G)$▫ we mean the intersection of all maximum independent sets. The independence ... number ▫$\alpha(G)$▫ is the cardinality of a maximum independent set, while ▫$\mu(G)$▫ is the size of a maximum matching in ▫$G$▫. A connected graph having only one cycle, say ▫$C$▫, is a unicyclic graph. In this paper we prove that if ▫$G$▫ is a unicyclic graph of order ▫$n$▫ and T$n - 1 = \alpha(G) + \mu(G)$T, then core▫$(G)$▫ coincides with the union of cores of all trees in ▫$G - C$▫.Source: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 5, no. 2, 2012, str. 325-331)Type of material - article, component partPublish date - 2012Language - englishCOBISS.SI-ID - 16277849
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Mandrescu, Eugen | ![]() |
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