Transitivity in some graph-classes

Subhabrata Paul () and Kamal Santra ()
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Subhabrata Paul: IIT Patna
Kamal Santra: IIT Patna

Journal of Combinatorial Optimization, 2025, vol. 50, issue 3, No 7, 29 pages

Abstract: Abstract Let $$G=(V, E)$$ be a graph, where V and E are the vertex and edge sets, respectively. For two disjoint subsets A and B of V, we say A dominates B if every vertex of B is adjacent to at least one vertex of A in G. A vertex partition $$\pi = \{V_1, V_2, \ldots , V_k\}$$ of G is called a transitive partition of size k if $$V_i$$ dominates $$V_j$$ for all i, j, where $$1\le i

Keywords: Transitivity; Split graphs; Nordhaus-Gaddum relations; Central graphs; Transitively critical graphs; MSC 05C69; MSC 05C70; MSC 05C85. (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01359-3

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