Displaying similar documents to “A note on cyclic chromatic number”

Linear and cyclic radio k-labelings of trees

Mustapha Kchikech, Riadh Khennoufa, Olivier Togni (2007)

Discussiones Mathematicae Graph Theory

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Motivated by problems in radio channel assignments, we consider radio k-labelings of graphs. For a connected graph G and an integer k ≥ 1, a linear radio k-labeling of G is an assignment f of nonnegative integers to the vertices of G such that | f ( x ) - f ( y ) | k + 1 - d G ( x , y ) , for any two distinct vertices x and y, where d G ( x , y ) is the distance between x and y in G. A cyclic k-labeling of G is defined analogously by using the cyclic metric on the labels. In both cases, we are interested in minimizing the span of the labeling....

Note on cyclic decompositions of complete bipartite graphs into cubes

Dalibor Fronček (1999)

Discussiones Mathematicae Graph Theory

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So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes Q d of a given dimension d was K d 2 d - 1 , d 2 d - 2 . We improve this result and show that also K d 2 d - 2 , d 2 d - 2 allows a cyclic decomposition into Q d . We also present a cyclic factorization of K 8 , 8 into Q₄.

Circles passing through five or more integer points

Shaunna M. Plunkett-Levin (2013)

Acta Arithmetica

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We find an improvement to Huxley and Konyagin’s current lower bound for the number of circles passing through five integer points. We conjecture that the improved lower bound is the asymptotic formula for the number of circles passing through five integer points. We generalise the result to circles passing through more than five integer points, giving the main theorem in terms of cyclic polygons with m integer point vertices. Theorem. Let m ≥ 4 be a fixed integer. Let W m ( R ) be the number...

Subnormality and cyclicity

Franciszek Hugon Szafraniec (2005)

Banach Center Publications

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For an unbounded operator S the question whether its subnormality can be built up from that of every S f , the restriction of S to a cyclic space generated by f in the domain of S, is analyzed. Though the question at large has been left open some partial results are presented and a possible way to prove it is suggested as well.

A note on another construction of graphs with 4 n + 6 vertices and cyclic automorphism group of order 4 n

Peteris Daugulis (2017)

Archivum Mathematicum

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The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having 4 n + 6 vertices and automorphism group cyclic of order 4 n , n 1 . As a special case we get graphs with 2 k + 6 vertices and cyclic automorphism groups of order 2 k . It can revive interest in related problems.

Strictly cyclic algebra of operators acting on Banach spaces H p ( β )

Bahmann Yousefi (2004)

Czechoslovak Mathematical Journal

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Let { β ( n ) } n = 0 be a sequence of positive numbers and 1 p < . We consider the space H p ( β ) of all power series f ( z ) = n = 0 f ^ ( n ) z n such that n = 0 | f ^ ( n ) | p β ( n ) p < . We investigate strict cyclicity of H p ( β ) , the weakly closed algebra generated by the operator of multiplication by z acting on H p ( β ) , and determine the maximal ideal space, the dual space and the reflexivity of the algebra H p ( β ) . We also give a necessary condition for a composition operator to be bounded on H p ( β ) when H p ( β ) is strictly cyclic.

Localization of jumps of the point-distinguishing chromatic index of K n , n

Mirko Horňák, Roman Soták (1997)

Discussiones Mathematicae Graph Theory

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The point-distinguishing chromatic index of a graph represents the minimum number of colours in its edge colouring such that each vertex is distinguished by the set of colours of edges incident with it. Asymptotic information on jumps of the point-distinguishing chromatic index of K n , n is found.

Kannan-type cyclic contraction results in 2 -Menger space

Binayak S. Choudhury, Samir Kumar BHANDARI (2016)

Mathematica Bohemica

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In this paper we establish Kannan-type cyclic contraction results in probabilistic 2-metric spaces. We use two different types of t -norm in our theorems. In our first theorem we use a Hadzic-type t -norm. We use the minimum t -norm in our second theorem. We prove our second theorem by different arguments than the first theorem. A control function is used in our second theorem. These results generalize some existing results in probabilistic 2-metric spaces. Our results are illustrated with...

On the index of length four minimal zero-sum sequences

Caixia Shen, Li-meng Xia, Yuanlin Li (2014)

Colloquium Mathematicae

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Let G be a finite cyclic group. Every sequence S over G can be written in the form S = ( n g ) · . . . · ( n l g ) where g ∈ G and n , . . . , n l i [ 1 , o r d ( g ) ] , and the index ind(S) is defined to be the minimum of ( n + + n l ) / o r d ( g ) over all possible g ∈ G such that ⟨g⟩ = G. A conjecture says that every minimal zero-sum sequence of length 4 over a finite cyclic group G with gcd(|G|,6) = 1 has index 1. This conjecture was confirmed recently for the case when |G| is a product of at most two prime powers. However, the general case is still open. In this paper,...

Cyclic Type Fixed Point Results in 2-Menger Spaces

Binayak S. CHOUDHURY, Samir Kumar BHANDARI, Parbati SAHA (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we introduce generalized cyclic contractions through r number of subsets of a probabilistic 2-metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t -norm. In another theorem we use a control function with minimum t -norm. Our results generalizes some existing fixed point theorem in 2-Menger spaces. The results are supported with some examples.

Bounded point evaluations for multicyclic operators

M. EL Guendafi, M. Mbekhta, E. H. Zerouali (2005)

Banach Center Publications

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Let T be a multicyclic operator defined on some Banach space. Bounded point evaluations and analytic bounded point evaluations for T are defined to generalize the cyclic case. We extend some known results on cyclic operators to the more general setting of multicyclic operators on Banach spaces. In particular we show that if T satisfies Bishop’s property (β), then a = σ a p ( T ) . We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept...

On light subgraphs in plane graphs of minimum degree five

Stanislav Jendrol&amp;#039;, Tomáš Madaras (1996)

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 well known that a plane graph of minimum degree five contains light edges and light triangles. In this paper we show that every plane graph of minimum degree five contains also light stars K 1 , 3 and K 1 , 4 and a light 4-path P₄. The results obtained for K 1 , 3 and P₄ are best possible.

Graceful signed graphs

Mukti Acharya, Tarkeshwar Singh (2004)

Czechoslovak Mathematical Journal

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A ( p , q ) -sigraph S is an ordered pair ( G , s ) where G = ( V , E ) is a ( p , q ) -graph and s is a function which assigns to each edge of G a positive or a negative sign. Let the sets E + and E - consist of m positive and n negative edges of G , respectively, where m + n = q . Given positive integers k and d , S is said to be ( k , d ) -graceful if the vertices of G can be labeled with distinct integers from the set { 0 , 1 , , k + ( q - 1 ) d } such that when each edge u v of G is assigned the product of its sign and the absolute difference of the integers assigned to...