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The generalized 3-edge-connectivity of lexicographic product graphs
The generalized -edge-connectivity of a graph is a
generalization of the concept of edge-connectivity. The lexicographic product
of two graphs and , denoted by , is an important graph
product. In this paper, we mainly study the generalized 3-edge-connectivity of
, and get upper and lower bounds of .
Moreover, all bounds are sharp.Comment: 14 page
The generalized 3-connectivity of Lexicographic product graphs
The generalized -connectivity of a graph , introduced by
Chartrand et al., is a natural and nice generalization of the concept of
(vertex-)connectivity. In this paper, we prove that for any two connected
graphs and , . We also give
upper bounds for and . Moreover, all
the bounds are sharp.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1103.609
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