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- W2175268523 abstract "A 3−arc of a graph G is a 4-tuple (y, a, b, x) of vertices such that both (y, a, b) and (a, b, x) are paths of length two in G. Let ←→G denote the symmetric digraph of a graph G. The 3-arc graph X(G) of a given graph G is defined to have vertices the arcs of ←→G. Two vertices (ay), (bx) are adjacent in X(G) if and only if (y, a, b, x) is a 3-arc of G. The purpose of this work is to study the edge-connectivity and restricted edge-connectivity of 3-arc graphs.We prove that the 3-arc graph X(G) of every connected graph G of minimum degree δ(G) ≥ 3 has edge-connectivity λ(X(G)) ≥ (δ(G) − 1)2; and restricted edge- connectivity λ(2)(X(G)) ≥ 2(δ(G) − 1)2 − 2 if κ(G) ≥ 2. We also provide examples showing that all these bounds are sharp." @default.
- W2175268523 created "2016-06-24" @default.
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- W2175268523 date "2011-01-01" @default.
- W2175268523 modified "2023-10-17" @default.
- W2175268523 title "On the connectivity and restricted edge-connectivity of 3-arc graphs" @default.
- W2175268523 hasPublicationYear "2011" @default.
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