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Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs

100%
Sun Y.
Discussiones Mathematicae Graph Theory
|
2016
|
tom 36
|
nr 4
833-843
EN
The generalized k-connectivity κk(G) of a graph G was introduced by Hager in 1985. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized k-edge-connectivity which is defined as λk(G) = min{λ(S) : S ⊆ V (G) and |S| = k}, where λ(S) denote the maximum number ℓ of pairwise edge-disjoint trees T1, T2, . . . , Tℓ in G such that S ⊆ V (Ti) for 1 ≤ i ≤ ℓ. In this paper, we study the generalized edge- connectivity of product graphs and obtain sharp upper bounds for the generalized 3-edge-connectivity of Cartesian product graphs and strong product graphs. Among our results, some special cases are also discussed.
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Minimal cycle bases of the lexicographic product of graphs

100%
Jaradat M.
Discussiones Mathematicae Graph Theory
|
2008
|
tom 28
|
nr 2
229-247
EN
A construction of minimum cycle bases of the lexicographic product of graphs is presented. Moreover, the length of a longest cycle of a minimal cycle basis is determined.
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Union of Distance Magic Graphs

63%
Cichacz S., Nikodem M.
Discussiones Mathematicae Graph Theory
|
2017
|
tom 37
|
nr 1
239-249
EN
A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ from V to the set {1, . . . , n} such that the weight w(x) = ∑y∈NG(x) ℓ(y) of every vertex x ∈ V is equal to the same element μ, called the magic constant. In this paper, we study unions of distance magic graphs as well as some properties of such graphs.
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