Results 31 to 40 of about 167 (98)
Decomposing 10-Regular Graphs into Paths of Length 5
Discussiones Mathematicae Graph Theory, 2022 Let G be a 10-regular graph which does not contain any 4-cycles. In this paper, we prove that G can be decomposed into paths of length 5, such that every vertex is a terminal of exactly two paths.
Xie Mengmeng, Zhou Chuixiang
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Strong edge geodetic problem in networks
Open Mathematics, 2017 Geodesic covering problems form a widely researched topic in graph theory. One such problem is geodetic problem introduced by Harary et al. [Math. Comput. Modelling, 1993, 17, 89-95].
Manuel Paul +4 more
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Covering the Edges of a Random Hypergraph by Cliques
Discussiones Mathematicae Graph Theory, 2022 We determine the order of magnitude of the minimum clique cover of the edges of a binomial, r-uniform, random hypergraph G(r)(n, p), p fixed. In doing so, we combine the ideas from the proofs of the graph case (r = 2) in Frieze and Reed [Covering the ...
Rödl Vojtěch, Ruciński Andrzej
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SIMPLE GRAPHOIDAL COVERING NUMBER OF PRODUCT OF GRAPHS
, 2016 A graphoidal cover of G is a set ψ of (not necessarily open) paths in G, such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ and every edge of G is in exactly one path in ψ.
G. V. Narayanan, J. Suseela, R. Kala
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Graceful Labeling of some Join Graphs and the Subdivision of Complete Bipartite Graphs
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.The join of graphs G and H, denoted by G + H, is the graph obtained from the disjoint union of G and H by joining each vertex in G to each vertex in H. An edge uw is said to be subdivided if uw is replaced by the path P : uvw, where v is the new vertex.
A. Panpa +3 more
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Discussiones Mathematicae Graph Theory, 2017 We characterize the class L32$L_3^2 $ of intersection graphs of hypergraphs with rank at most 3 and multiplicity at most 2 by means of a finite list of forbidden induced subgraphs in the class of threshold graphs.
Metelsky Yury +2 more
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Packing Trees in Complete Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2022 An embedding of a graph H in a graph G is an injection (i.e., a one-to-one function) σ from the vertices of H to the vertices of G such that σ(x)σ(y) is an edge of G for all edges xy of H. The image of H in G under σ is denoted by σ(H).
Wang Jieyan
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Graceful Labeling of Spider Graphs With at Most Five Legs
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.A graceful labeling of a graph G with q edges is an injection f from the vertices of G to the set {0, 1, ⋯, q} such that, when each edge uv is assigned the label |f(u) − f(v)|, the resulting edge labels are distinct. A spider graph is a tree with exactly one vertex of degree greater than 2, and this vertex is called the branch vertex. A leg of a spider
A. Panpa +3 more
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The harmonic index for unicyclic and bicyclic graphs with given matching number
, 2015 The harmonic index of a graph G is defined as the sum of the weights 2 d.u/Cd.v/ of all edges uv of G, where d.u/ denotes the degree of a vertex u in G.
Lingping Zhong
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Decomposition of the Product of Cycles Based on Degree Partition
Discussiones Mathematicae Graph Theory, 2019 The Cartesian product of n cycles is a 2n-regular, 2n-connected and bi- pancyclic graph. Let G be the Cartesian product of n even cycles and let 2n = n1+ n2+ ・ ・ ・ + nkwith k ≥ 2 and ni≥ 2 for each i. We prove that if k = 2, then G can be decomposed into
Borse Y. M., Shaikh S. R.
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