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Criticality of Switching Classes of Reversible 2-Structures Labeled by an Abelian Group

Houmem Belkhechine, Pierre Ille, Robert E. Woodrow (2017)

Discussiones Mathematicae Graph Theory

Let V be a finite vertex set and let (, +) be a finite abelian group. An -labeled and reversible 2-structure defined on V is a function g : (V × V) (v, v) : v ∈ V → such that for distinct u, v ∈ V, g(u, v) = −g(v, u). The set of -labeled and reversible 2-structures defined on V is denoted by ℒ(V, ). Given g ∈ ℒ(V, ), a subset X of V is a clan of g if for any x, y ∈ X and v ∈ V X, g(x, v) = g(y, v). For example, ∅, V and v (for v ∈ V) are clans of g, called trivial. An element g of ℒ(V, ) is primitive...

Crossing numbers and cutwidths.

Djidjev, Hristo N., Vrt'o, Imrich (2003)

Journal of Graph Algorithms and Applications

Crossings, colorings, and cliques.

Albertson, Michael O., Cranston, Daniel W., Fox, Jacob (2009)

The Electronic Journal of Combinatorics [electronic only]

Cubic Cayley graphs with small diameter.

Curtin, Eugen (2001)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

Cubic edge-transitive graphs of order $4 p^{2}$ .

Alaeiyan, M., Onagh, B.N. (2009)

Acta Mathematica Universitatis Comenianae. New Series

Cubic graphs without a Petersen minor have nowhere-zero 5-flow.

Kochol, M. (1999)

Acta Mathematica Universitatis Comenianae. New Series

Cubic Moore Graphs

Juraj Bosák (1970)

Matematický časopis

Cubic partial cubes from simplicial arrangements.

Eppstein, David (2006)

The Electronic Journal of Combinatorics [electronic only]

Curvature on a graph via its geometric spectrum

Paul Baird (2013)

Actes des rencontres du CIRM

We approach the problem of defining curvature on a graph by attempting to attach a ‘best-fit polytope’ to each vertex, or more precisely what we refer to as a configured star. How this should be done depends upon the global structure of the graph which is reflected in its geometric spectrum. Mean curvature is the most natural curvature that arises in this context and corresponds to local liftings of the graph into a suitable Euclidean space. We discuss some examples.

Cut-off for large sums of graphs

Bernard Ycart (2007)

Annales de l’institut Fourier

If $L$ is the combinatorial Laplacian of a graph, $exp (- L t)$ converges to a matrix with identical coefficients. The speed of convergence is measured by the maximal entropy distance. When the graph is the sum of a large number of components, a cut-off phenomenon may occur: before some instant the distance to equilibrium tends to infinity; after that instant it tends to $0$ . A sufficient condition for cut-off is given, and the cut-off instant is expressed as a function of the gap and eigenvectors of components....

Cutpoints, lobes and the spectra of graphs

Grone, Robert, Merris, Russell (1988)

Portugaliae mathematica

Cutthroat, an all-small game on graphs.

McCurdy, Sarah K., Nowakowski, Richard J. (2005)

Integers

Cut-vertices and domination in graphs

Preben Dahl Vestergaard, Bohdan Zelinka (1995)

Mathematica Bohemica

The paper studies the domatic numbers and the total domatic numbers of graphs having cut-vertices.

Cutwidth of iterated caterpillars

Lan Lin, Yixun Lin (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The cutwidth is an important graph-invariant in circuit layout designs. The cutwidth of a graph G is the minimum value of the maximum number of overlap edges when G is embedded into a line. A caterpillar is a tree which yields a path when all its leaves are removed. An iterated caterpillar is a tree which yields a caterpillar when all its leaves are removed. In this paper we present an exact formula for the cutwidth of the iterated caterpillars.

Cutwidth of the de Bruijn graph

André Raspaud, Ondrej Sýkora, Imrich Vrt'o (1995)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Cutwidth of the $r$ -dimensional mesh of $d$ -ary trees

Imrich Vrťo (2000)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Cutwidth of the r-dimensional Mesh of d-ary Trees

Imrich Vrťo (2010)

RAIRO - Theoretical Informatics and Applications

We prove that the cutwidth of the r-dimensional mesh of d-ary trees is of order $Θ (d^{(r - 1) n + 1})$ , which improves and generalizes previous results.

Cycle and path embedding on 5-ary N-cubes

Tsong-Jie Lin, Sun-Yuan Hsieh, Hui-Ling Huang (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study two topological properties of the 5-ary $n$ -cube $Q_{n}^{5}$ . Given two arbitrary distinct nodes $x$ and $y$ in $Q_{n}^{5}$ , we prove that there exists an $x$ - $y$ path of every length ranging from $2 n$ to $5^{n} - 1$ , where $n \geq 2$ . Based on this result, we prove that $Q_{n}^{5}$ is 5-edge-pancyclic by showing that every edge in $Q_{n}^{5}$ lies on a cycle of every length ranging from $5$ to $5^{n}$ .

Cycle and Path Embedding on 5-ary N-cubes

Tsong-Jie Lin, Sun-Yuan Hsieh, Hui-Ling Huang (2008)

RAIRO - Theoretical Informatics and Applications

We study two topological properties of the 5-ary n-cube $Q_{n}^{5}$ . Given two arbitrary distinct nodes x and y in $Q_{n}^{5}$ , we prove that there exists an x-y path of every length ranging from 2n to 5n - 1, where n ≥ 2. Based on this result, we prove that $Q_{n}^{5}$ is 5-edge-pancyclic by showing that every edge in $Q_{n}^{5}$ lies on a cycle of every length ranging from 5 to 5n.

Cycle Double Covers of Infinite Planar Graphs

Mohammad Javaheri (2016)

Discussiones Mathematicae Graph Theory

In this paper, we study the existence of cycle double covers for infinite planar graphs. We show that every infinite locally finite bridgeless k-indivisible graph with a 2-basis admits a cycle double cover.

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