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

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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.

The fundamental group of a locally finite graph with ends-a hyperfinite approach

Isaac Goldbring, Alessandro Sisto (2016)

Fundamenta Mathematicae

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The end compactification |Γ| of a locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π₁(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also show how to recover the standard description of π₁(|Γ|) given by Diestel and Sprüssel (2011). Finally,...

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...

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:...

The periphery graph of a median graph

Boštjan Brešar, Manoj Changat, Ajitha R. Subhamathi, Aleksandra Tepeh (2010)

Discussiones Mathematicae Graph Theory

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The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are...

Random threshold graphs.

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

The Electronic Journal of Combinatorics [electronic only]

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