Displaying similar documents to “Recognizing weighted directed cartesian graph bundles”

On k -strong distance in strong digraphs

Ping Zhang (2002)

Mathematica Bohemica

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For a nonempty set S of vertices in a strong digraph D , the strong distance d ( S ) is the minimum size of a strong subdigraph of D containing the vertices of S . If S contains k vertices, then d ( S ) is referred to as the k -strong distance of S . For an integer k ≥ 2 and a vertex v of a strong digraph D , the k -strong eccentricity s e k ( v ) of v is the maximum k -strong distance d ( S ) among all sets S of k vertices in D containing v . The minimum k -strong eccentricity among the vertices of D is its k -strong radius...

Digraphs with isomorphic underlying and domination graphs: connected U G c ( d )

Kim A.S. Factor, Larry J. Langley (2007)

Discussiones Mathematicae Graph Theory

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The domination graph of a directed graph has an edge between vertices x and y provided either (x,z) or (y,z) is an arc for every vertex z distinct from x and y. We consider directed graphs D for which the domination graph of D is isomorphic to the underlying graph of D. We demonstrate that the complement of the underlying graph must have k connected components isomorphic to complete graphs, paths, or cycles. A complete characterization of directed graphs where k = 1 is presented. ...

A σ₃ type condition for heavy cycles in weighted graphs

Shenggui Zhang, Xueliang Li, Hajo Broersma (2001)

Discussiones Mathematicae Graph Theory

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A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree d w ( v ) of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions: 1. The weighted degree sum of any three independent vertices is at least m; 2. w(xz) = w(yz)...

Arc-transitive and s-regular Cayley graphs of valency five on Abelian groups

Mehdi Alaeiyan (2006)

Discussiones Mathematicae Graph Theory

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Let G be a finite group, and let 1 G ∉ S ⊆ G . A Cayley di-graph Γ = Cay(G,S) of G relative to S is a di-graph with a vertex set G such that, for x,y ∈ G, the pair (x,y) is an arc if and only if y x - 1 ∈ S . Further, if S = S - 1 : = s - 1 | s ∈ S , then Γ is undirected. Γ is conected if and only if G = ⟨s⟩. A Cayley (di)graph Γ = Cay(G,S) is called normal if the right regular representation of G is a normal subgroup of the automorphism group of Γ. A graph Γ is said to be arc-transitive, if Aut(Γ) is transitive on an arc set. Also,...