Graphs with odd and even distances between non-cut vertices

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dc.contributor.authorAntoshyna, Katerynaen_US
dc.contributor.authorKozerenko, Sergiy
dc.date.accessioned2025-03-12T12:59:26Z
dc.date.available2025-03-12T12:59:26Z
dc.date.issued2025
dc.description.abstractWe prove that in a connected graph, the distances between non-cut vertices are odd if and only if it is the line graph of a strong unique independence tree. We then show that any such tree can be inductively constructed from stars using a simple operation. Further, we study the connected graphs in which the distances between non-cut vertices are even (shortly, NCE-graphs). Our main results on NCE-graphs are the following: we give a criterion of NCE-graphs, show that any bipartite graph is an induced subgraph of an NCE-graph, characterize NCE-graphs with exactly two leaves, characterize graphs that can be subdivided to NCE-graphs, and provide a characterization for NCE-graphs which are maximal with respect to the edge addition operation.en_US
dc.identifier.citationAntoshyna K. Graphs with odd and even distances between non-cut vertices / Kateryna Antoshyna, Sergiy Kozerenko // Opuscula Mathematica. - 2025. - Vol. 45, Issue 1. - P. 5-25. - https://doi.org/10.7494/OpMath.2025.45.1.5en_US
dc.identifier.issn1232−9274
dc.identifier.issn2300−6919
dc.identifier.urihttps://doi.org/10.7494/OpMath.2025.45.1.5
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/33918
dc.language.isoenen_US
dc.relation.sourceOpuscula Mathematicaen_US
dc.statusfirst publisheden_US
dc.subjectnon-cut vertexen_US
dc.subjectgraph distanceen_US
dc.subjectline graphen_US
dc.subjectblocken_US
dc.subjectstrong unique independence treeen_US
dc.subjectarticleen_US
dc.titleGraphs with odd and even distances between non-cut verticesen_US
dc.typeArticleen_US
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