Results 61 to 70 of about 269 (132)
Chromatic Properties of the Pancake Graphs
Discussiones Mathematicae Graph Theory, 2017 Chromatic properties of the Pancake graphs Pn, n ⩾ 2, that are Cayley graphs on the symmetric group Symn generated by prefix-reversals are investigated in the paper.
Konstantinova Elena
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Linear List Coloring of Some Sparse Graphs
Discussiones Mathematicae Graph Theory, 2021 A linear k-coloring of a graph is a proper k-coloring of the graph such that any subgraph induced by the vertices of any pair of color classes is a union of vertex-disjoint paths. A graph G is linearly L-colorable if there is a linear coloring c of G for
Chen Ming, Li Yusheng, Zhang Li
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Conflict-Free Vertex Connection Number At Most 3 and Size of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in a vertex-coloured graph is called conflict-free if there is a colour used on exactly one of its vertices. A vertex-coloured graph is said to be conflict-free vertex-connected if any two distinct vertices of the graph are connected by a conflict-
Doan Trung Duy, Schiermeyer Ingo
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An Improved Upper Bound on Neighbor Expanded Sum Distinguishing Index
Discussiones Mathematicae Graph Theory, 2020 A total k-weighting f of a graph G is an assignment of integers from the set {1, . . . , k} to the vertices and edges of G. We say that f is neighbor expanded sum distinguishing, or NESD for short, if Σw∈N(v) (f(vw) + f(w)) differs from Σw∈N(u)(f(uw) + f(
Vučković Bojan
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Note on group irregularity strength of disconnected graphs
Open Mathematics, 2018 We investigate the group irregularity strength (sg(G)) of graphs, i.e. the smallest value of s such that taking any Abelian group 𝓖 of order s, there exists a function f : E(G) → 𝓖 such that the sums of edge labels at every vertex are distinct. So far it
Anholcer Marcin +3 more
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More on the Minimum Size of Graphs with Given Rainbow Index
Discussiones Mathematicae Graph Theory, 2020 The concept of k-rainbow index rxk(G) of a connected graph G, introduced by Chartrand et al., is a natural generalization of the rainbow connection number of a graph.
Zhao Yan
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Extended Keller Graph and its properties
, 2019 In the paper extended Keller graph Γ3d is defined and some of its properties, such as Hamiltonian, the independence number, the chromatic number, etc.,are proved. Moreover, the size of a maximum clique of Γ3d for d = 2, 3, 4 and d ≥ 8 is given and for d =
Lysakowska, Magdalena
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Edge-face total chromatic number of 3-regular Halin graphs, Congressus Numerantium
, 2000 A Halin graph is a plane graph H = T ∪ C, where T is a plane tree with no vertex of degree two and at least one vertex of degree three or more, and C is a cycle connecting the end vertices of T in the cyclic order determined by a plane embedment of T. In
Wai Chee Shiu +3 more
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An introduction to the k-defect polynomials
, 2019 The 0-defect polynomial of a graph is just the chromatic polynomial. This polynomial has been widely studied in the literature. Yet little is known about the properties of k-defect polynomials of graphs in general, when 0 < k ≤ |E(G)|.
Mphako-Banda, Eunice
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Sum-List Colouring of Unions of a Hypercycle and a Path with at Most Two Vertices in Common
Discussiones Mathematicae Graph Theory, 2020 Given a hypergraph and a function f : V () → , we say that is f-choosable if there is a proper vertex colouring ϕ of such that ϕ (v) ∈ L(v) for all v ∈ V (), where L : V () → 2 is any assignment of f(v) colours to a vertex v.
Drgas-Burchardt Ewa +1 more
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