Displaying similar documents to “Monochromatic kernel-perfectness of special classes of digraphs”

On a problem of E. Prisner concerning the biclique operator

Bohdan Zelinka (2002)

Mathematica Bohemica

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The symbol K ( B , C ) denotes a directed graph with the vertex set B ∪ C for two (not necessarily disjoint) vertex sets B , C in which an arc goes from each vertex of B into each vertex of C . A subdigraph of a digraph D which has this form is called a bisimplex in D . A biclique in D is a bisimplex in D which is not a proper subgraph of any other and in which B ≠ ∅ and C ≠ ∅ . The biclique digraph C → ( D ) of D is the digraph whose vertex set is the set of all bicliques in D and in which there is an arc from K ( B 1 , C 1 ) into K ( B 2 , C 2 ) ...

The classification of finite groups by using iteration digraphs

Uzma Ahmad, Muqadas Moeen (2016)

Czechoslovak Mathematical Journal

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A digraph is associated with a finite group by utilizing the power map f : G → G defined by f ( x ) = x k for all x ∈ G , where k is a fixed natural number. It is denoted by γ G ( n , k ) . In this paper, the generalized quaternion and 2 -groups are studied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a 2 -group are determined for a 2 -group to be a generalized quaternion group. Further, the classification of two generated 2 -groups as abelian...

Signed domination and signed domatic numbers of digraphs

Lutz Volkmann (2011)

Discussiones Mathematicae Graph Theory

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Let D be a finite and simple digraph with the vertex set V(D), and let f:V(D) → -1,1 be a two-valued function. If ∑ x ∈ N ¯ [ v ] f ( x ) ≥ 1 for each v ∈ V(D), where N¯[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V(D)) is called the weight w(f) of f. The minimum of weights w(f), taken over all signed dominating functions f on D, is the signed domination number γ S ( D ) of D. A set f ₁ , f ₂ , . . . , f d of signed dominating functions on D with the property that...

Decompositions of nearly complete digraphs into t isomorphic parts

Mariusz Meszka, Zdzisław Skupień (2009)

Discussiones Mathematicae Graph Theory

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An arc decomposition of the complete digraph Kₙ into t isomorphic subdigraphs is generalized to the case where the numerical divisibility condition is not satisfied. Two sets of nearly tth parts are constructively proved to be nonempty. These are the floor tth class ( Kₙ-R)/t and the ceiling tth class ( Kₙ+S)/t, where R and S comprise (possibly copies of) arcs whose number is the smallest possible. The existence of cyclically 1-generated decompositions of Kₙ into cycles → C n - 1 and into paths...

Monotonically normal e -separable spaces may not be perfect

John E. Porter (2018)

Commentationes Mathematicae Universitatis Carolinae

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A topological space X is said to be e -separable if X has a σ -closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that e -separable PIGO spaces are perfect and asked if e -separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of e -separable monotonically normal spaces which are not perfect. Extremely normal e -separable spaces are shown to be stratifiable.

Self-diclique circulant digraphs

Marietjie Frick, Bernardo Llano, Rita Zuazua (2015)

Mathematica Bohemica

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We study a particular digraph dynamical system, the so called digraph diclique operator. Dicliques have frequently appeared in the literature the last years in connection with the construction and analysis of different types of networks, for instance biochemical, neural, ecological, sociological and computer networks among others. Let D = ( V , A ) be a reflexive digraph (or network). Consider X and Y (not necessarily disjoint) nonempty subsets of vertices (or nodes) of D . A disimplex K ( X , Y ) of D is...

Majority choosability of 1-planar digraph

Weihao Xia, Jihui Wang, Jiansheng Cai (2023)

Czechoslovak Mathematical Journal

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A majority coloring of a digraph D with k colors is an assignment π : V ( D ) → { 1 , 2 , ⋯ , k } such that for every v ∈ V ( D ) we have π ( w ) = π ( v ) for at most half of all out-neighbors w ∈ N + ( v ) . A digraph D is majority k -choosable if for any assignment of lists of colors of size k to the vertices, there is a majority coloring of D from these lists. We prove that if U ( D ) is a 1-planar graph without a 4-cycle, then D is majority 3-choosable. And we also prove that every NIC-planar digraph is majority 3-choosable.