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Displaying 221 – 240 of 428

On connectedness of graphs on direct product of Weyl groups

Samy A. Youssef, S. G. Hulsurkar (1995)

Archivum Mathematicum

In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected iff the graph on each factor of the direct product is connected.

On connectedness of graphs on Weyl groups of type $A_{n}$ ( $n \geq 4$ )

Samy A. Youssef, S. G. Hulsurkar (1995)

Archivum Mathematicum

On connection between the structure of a finite group and the properties of its prime graph.

Vasil'ev, A.V. (2005)

Sibirskij Matematicheskij Zhurnal

On distinguishing and distinguishing chromatic numbers of hypercubes

Werner Klöckl (2008)

Discussiones Mathematicae Graph Theory

The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d colors that is not preserved by any nontrivial automorphism. The restriction to proper labelings leads to the definition of the distinguishing chromatic number $χ_{D} (G)$ of G. Extending these concepts to infinite graphs we prove that $D (Q_{ℵ} ₀) = 2$ and $χ_{D} (Q_{ℵ} ₀) = 3$ , where $Q_{ℵ} ₀$ denotes the hypercube of countable dimension. We also show that $χ_{D} (Q ₄) = 4$ , thereby completing the investigation of finite hypercubes with respect to $χ_{D}$ . Our results...

On double coverings of some rotary hypermaps.

Breda, Ana, d'Azevedo, Antonio Breda, Catalano, Domenico (2009)

Beiträge zur Algebra und Geometrie

On double covers of graphs

Bohdan Zelinka (1982)

Mathematica Slovaca

On $f$ -edge cover coloring of nearly bipartite graphs.

Li, Jinbo, Liu, Guizhen (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

On Finite Groups Generated by Odd Transpositions. I.

Michael Aschbacher (1972)

Mathematische Zeitschrift

On finite homomorphic images of the multiplicative group of a division algebra.

Segev, Yoav (1999)

Annals of Mathematics. Second Series

On Graphical Regular Representations of Direct Products of Groups.

M.E. Watkins, Lewis A. Nowitz (1972)

Monatshefte für Mathematik

On infinite tournaments with regular automorphism groups.

D.A. Holton, Mark E. Watkins (1981)

Aequationes mathematicae

On iteration digraph and zero-divisor graph of the ring $ℤ_{n}$

Tengxia Ju, Meiyun Wu (2014)

Czechoslovak Mathematical Journal

In the first part, we assign to each positive integer $n$ a digraph $Γ (n, 5),$ whose set of vertices consists of elements of the ring $ℤ_{n} = {0, 1, \dots, n - 1}$ with the addition and the multiplication operations modulo $n,$ and for which there is a directed edge from $a$ to $b$ if and only if $a^{5} \equiv b (mod n)$ . Associated with $Γ (n, 5)$ are two disjoint subdigraphs: $Γ_{1} (n, 5)$ and $Γ_{2} (n, 5)$ whose union is $Γ (n, 5) .$ The vertices of $Γ_{1} (n, 5)$ are coprime to $n,$ and the vertices of $Γ_{2} (n, 5)$ are not coprime to $n .$ In this part, we study the structure of $Γ (n, 5)$ in detail. In the second part, we investigate the zero-divisor...

On $k$ -walk-regular graphs.

Dalfó, C., Fiol, M.A., Garriga, E. (2009)

The Electronic Journal of Combinatorics [electronic only]

On L-ideal-based L-zero-divisor graphs

S. Ebrahimi Atani, M. Shajari Kohan (2011)

Discussiones Mathematicae - General Algebra and Applications

In a manner analogous to a commutative ring, the L-ideal-based L-zero-divisor graph of a commutative ring R can be defined as the undirected graph Γ(μ) for some L-ideal μ of R. The basic properties and possible structures of the graph Γ(μ) are studied.

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