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2. Adjacent vertex distinguishing total coloring of corona product of graphsHanna Furmańczyk, Rita Zuazua, 2025, original scientific article Abstract: An adjacent vertex distinguishing total k-coloring f of a graph G is a proper total k-coloring of G such that no pair of adjacent vertices has the same color sets, where the color set at a vertex v, C_f^G(v), is {f(v)} ∪ {f(vu)|u ∈ V(G), vu ∈ E(G)}. In 2005 Zhang et al. posted the conjecture (AVDTCC) that every simple graph G has adjacent vertex distinguishing total (Δ(G) + 3)-coloring. In this paper we confirm the conjecture for many types of coronas, in particular for generalized, simple and l-coronas of graphs, not relating the results to particular graph classes of the factors.
Keywords: corona graph, l-corona, generalized corona graph, adjacent vertex distinguishing total coloring, AVDTC Conjecture
Published in RUP: 21.10.2025; Views: 289; Downloads: 1
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3. Bonsma, Paul; Paulusma, Daniël: Using contracted solution graphs for solving reconfiguration problems. (English summary) Acta Inform. 56 (2019), no. 7-8, 619-648.Clément Jean Dallard, 2021, review, book review, critique Keywords: reconfiguration, dynamic programming, graph coloring
Published in RUP: 26.10.2021; Views: 3537; Downloads: 12
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6. Reconstructing perfect phylogenies via binary matrices, branchings in DAGs, and a generalization of Dilworth's theoremMartin Milanič, 2018, published scientific conference contribution abstract (invited lecture) Keywords: perfect phylogeny, NP-hard problem, graph coloring, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic
Published in RUP: 17.09.2018; Views: 3419; Downloads: 22
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7. Adjacency preservers, symmetric matrices, and coresMarko Orel, 2012, original scientific article Abstract: It is shown that the graph ▫$\Gamma_n$▫ that has the set of all ▫$n \times n$▫ symmetric matrices over a finite field as the vertex set, with two matrices being adjacent if and only if the rank of their difference equals one, is a core if ▫$n \ge 3$▫. Eigenvalues of the graph ▫$\Gamma_n$▫ are calculated as well.
Keywords: adjacency preserver, symmetric matrix, finite field, eigenvalue of a graph, coloring, quadratic form
Published in RUP: 15.10.2013; Views: 5422; Downloads: 149
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