A search for regular K3-irregular graphs
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Date
2024
Authors
Hak, Artem
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Abstract
For a given graph F, the F-degree of a vertex v in G is the number of subgraphs of G, isomorphic to F, to which v belongs. A graph G is called F-irregular if all vertices of G have distinct F-degrees. In [1], the existence of regular K3-irregular graphs was posed as an open question. Examples of such graphs for regularities r ∈ {10, 11, 12} were constructed in [2]. We analytically prove that no such graphs exist for r ≤ 7, present such a graph for r = 9, and establish bounds on the order for r = 8. We will use t(v) to denote the K3-degree.
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Keywords
K3-irregular graphs, graph F, subgraphs of G, conference abstracts
Citation
Hak A. A search for regular K3-irregular graphs / Artem Hak // Ukraine Mathematics Conference "At the End of the Year 2024", December 16–18, 2024 : book of abstracts / Taras Shevchenko National University of Kyiv, Institute of Mathematics of National Academy of Sciences of Ukraine. - Kyiv, 2024. - P. 30.