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Displaying similar documents to “Hexavalent ( G , s ) -transitive graphs”

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,...

Strong Transitivity and Graph Maps

Katsuya Yokoi (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study the relation between transitivity and strong transitivity, introduced by W. Parry, for graph self-maps. We establish that if a graph self-map f is transitive and the set of fixed points of f k is finite for each k ≥ 1, then f is strongly transitive. As a corollary, if a piecewise monotone graph self-map is transitive, then it is strongly transitive.

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...

Restrained domination in unicyclic graphs

Johannes H. Hattingh, Ernst J. Joubert, Marc Loizeaux, Andrew R. Plummer, Lucas van der Merwe (2009)

Discussiones Mathematicae Graph Theory

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Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S. The restrained domination number of G, denoted by γ r ( G ) , is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then γ r ( U ) ≥ ⎡ n / 3 ⎤ , and provide a characterization of graphs achieving this bound.

On Lee's conjecture and some results

Lixia Fan, Zhihe Liang (2009)

Discussiones Mathematicae Graph Theory

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S.M. Lee proposed the conjecture: for any n > 1 and any permutation f in S(n), the permutation graph P(Pₙ,f) is graceful. For any integer n > 1 and permutation f in S(n), we discuss the gracefulness of the permutation graph P(Pₙ,f) if f = ∏ k = 0 l - 1 ( m + 2 k , m + 2 k + 1 ) , and ∏ k = 0 l - 1 ( m + 4 k , m + 4 k + 2 ) ( m + 4 k + 1 , m + 4 k + 3 ) for any positive integers m and l.

Distance in stratified graphs

Gary Chartrand, Lisa Hansen, Reza Rashidi, Naveed Sherwani (2000)

Czechoslovak Mathematical Journal

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A graph G is stratified if its vertex set is partitioned into classes, called strata. If there are k strata, then G is k -stratified. These graphs were introduced to study problems in VLSI design. The strata in a stratified graph are also referred to as color classes. For a color X in a stratified graph G , the X -eccentricity e X ( v ) of a vertex v of G is the distance between v and an X -colored vertex furthest from v . The minimum X -eccentricity among the vertices of G is the X -radius r a d X G of G ...

More classes of non-orbit-transitive operators

Carl Pearcy, Lidia Smith (2010)

Studia Mathematica

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In [JKP] and its sequel [FPS] the authors initiated a program whose (announced) goal is to eventually show that no operator in ℒ(ℋ) is orbit-transitive. In [JKP] it is shown, for example, that if T ∈ ℒ(ℋ) and the essential (Calkin) norm of T is equal to its essential spectral radius, then no compact perturbation of T is orbit-transitive, and in [FPS] this result is extended to say that no element of this same class of operators is weakly orbit-transitive. In the present note we show...