Displaying similar documents to “Unimodular Pisot substitutions and their associated tiles”

Note on independent sets of a graph

Jaroslav Ivančo (1994)

Mathematica Bohemica

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Let the number of k -element sets of independent vertices and edges of a graph G be denoted by n ( G , k ) and m ( G , k ) , respectively. It is shown that the graphs whose every component is a circuit are the only graphs for which the equality n ( G , k ) = m ( G , k ) is satisfied for all values of k .

Système dynamique à spectre discret et pavage périodique associé à une substitution

Anne Siegel (2004)

Annales de l'Institut Fourier

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On donne une condition combinatoire effective suffisante pour que le sytème dynamique associé à une substitution de type Pisot ait un spectre purement discret. Dans le cas unimodulaire, cette condition est nécessaire dès que la substitution n'a qu'un cobord trivial ; elle est vérifiée si et seulement si le fractal de Rauzy associé à la substitution engendre un pavage auto-similaire et périodique. On en déduit des conditions de connexité des fractals de Rauzy....

Dense Arbitrarily Partitionable Graphs

Rafał Kalinowski, Monika Pilśniak, Ingo Schiermeyer, Mariusz Woźniak (2016)

Discussiones Mathematicae Graph Theory

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A graph G of order n is called arbitrarily partitionable (AP for short) if, for every sequence (n1, . . . , nk) of positive integers with n1 + ⋯ + nk = n, there exists a partition (V1, . . . , Vk) of the vertex set V (G) such that Vi induces a connected subgraph of order ni for i = 1, . . . , k. In this paper we show that every connected graph G of order n ≥ 22 and with [...] ‖G‖ > (n−42)+12 | | G | | > n - 4 2 + 12 edges is AP or belongs to few classes of exceptional graphs.

On the structure of plane graphs of minimum face size 5

Tomás Madaras (2004)

Discussiones Mathematicae Graph Theory

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A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is known that a plane graph of minimum face size 5 contains light paths and a light pentagon. In this paper we show that every plane graph of minimum face size 5 contains also a light star K 1 , 3 and we present a structural result concerning the existence of a pair of adjacent faces with degree-bounded vertices.

Metric dimension and zero forcing number of two families of line graphs

Linda Eroh, Cong X. Kang, Eunjeong Yi (2014)

Mathematica Bohemica

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Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the “AIM Minimum Rank–Special Graphs Work Group”, whereas metric dimension is a well-known graph parameter. We investigate the metric dimension and the zero forcing number of some line graphs by first determining the metric dimension and the zero forcing number of the line graphs of wheel graphs and the bouquet of circles. We prove that Z ( G ) 2 Z ( L ( G ) ) for a simple and connected...

The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition

Michael Keane, K. Károly, Boris Solomyak (2003)

Fundamenta Mathematicae

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Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.

Join of two graphs admits a nowhere-zero 3 -flow

Saieed Akbari, Maryam Aliakbarpour, Naryam Ghanbari, Emisa Nategh, Hossein Shahmohamad (2014)

Czechoslovak Mathematical Journal

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Let G be a graph, and λ the smallest integer for which G has a nowhere-zero λ -flow, i.e., an integer λ for which G admits a nowhere-zero λ -flow, but it does not admit a ( λ - 1 ) -flow. We denote the minimum flow number of G by Λ ( G ) . In this paper we show that if G and H are two arbitrary graphs and G has no isolated vertex, then Λ ( G H ) 3 except two cases: (i) One of the graphs G and H is K 2 and the other is 1 -regular. (ii) H = K 1 and G is a graph with at least one isolated vertex or a component whose every...

The graph polynomial and the number of proper vertex coloring

Michael Tarsi (1999)

Annales de l'institut Fourier

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Alon and Tarsi presented in a previous paper a certain weighted sum over the set of all proper k -colorings of a graph, which can be computed from its graph polynomial. The subject of this paper is another combinatorial interpretation of the same quantity, expressed in terms of the numbers of certain modulo k flows in the graph. Some relations between graph parameters can be obtained by combining these two formulas. For example: The number of proper 3-colorings of a 4-regular graph and...