Displaying similar documents to “On the number of representations of an element in a polygonal Cayley graph”

On the number of representations of an element in a polygonal Cayley graph

Gabriella Kuhn, Paolo M. Soardi (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We compute explicitly the number of paths of given length joining two vertices of the Cayley graph of the free product of cyclic groups of order k.

Random threshold graphs.

Reilly, Elizabeth Perez, Scheinerman, Edward R. (2009)

The Electronic Journal of Combinatorics [electronic only]

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Paired- and induced paired-domination in {E,net}-free graphs

Oliver Schaudt (2012)

Discussiones Mathematicae Graph Theory

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A dominating set of a graph is a vertex subset that any vertex belongs to or is adjacent to. Among the many well-studied variants of domination are the so-called paired-dominating sets. A paired-dominating set is a dominating set whose induced subgraph has a perfect matching. In this paper, we continue their study. We focus on graphs that do not contain the net-graph (obtained by attaching a pendant vertex to each vertex of the triangle) or the E-graph (obtained by...

A Note on Path Domination

Liliana Alcón (2016)

Discussiones Mathematicae Graph Theory

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We study domination between different types of walks connecting two non-adjacent vertices u and v of a graph (shortest paths, induced paths, paths, tolled walks). We succeeded in characterizing those graphs in which every uv-walk of one particular kind dominates every uv-walk of other specific kind. We thereby obtained new characterizations of standard graph classes like chordal, interval and superfragile graphs.

Minimal claw-free graphs

P. Dankelmann, Henda C. Swart, P. van den Berg, Wayne Goddard, M. D. Plummer (2008)

Czechoslovak Mathematical Journal

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A graph G is a minimal claw-free graph (m.c.f. graph) if it contains no K 1 , 3 (claw) as an induced subgraph and if, for each edge e of G , G - e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs.

Hamiltonicity in Partly claw-free graphs

Moncef Abbas, Zineb Benmeziane (2009)

RAIRO - Operations Research

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Matthews and Sumner have proved in [10] that if is a 2-connected claw-free graph of order such that /3, then is Hamiltonian. We say that a graph is almost claw-free if for every vertex of G, 〈 is 2-dominated and the set of centers of claws of is an independent set. Broersma [5] have proved that if is a 2-connected almost claw-free graph of order such that such that /3, then is Hamiltonian. We generalize these results by considering the graphs satisfying the following property:...

Path-Neighborhood Graphs

R.C. Laskar, Henry Martyn Mulder (2013)

Discussiones Mathematicae Graph Theory

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A path-neighborhood graph is a connected graph in which every neighborhood induces a path. In the main results the 3-sun-free path-neighborhood graphs are characterized. The 3-sun is obtained from a 6-cycle by adding three chords between the three pairs of vertices at distance 2. A Pk-graph is a path-neighborhood graph in which every neighborhood is a Pk, where Pk is the path on k vertices. The Pk-graphs are characterized for k ≤ 4.