Year 2019

• Weak Stability of Centred Quadratic Stochastic Operators

  Publication

  • K. Bartoszek
  • J. Domsta
  • M. Pułka

  - Bulletin of the Malaysian Mathematical Sciences Society - Year 2019

  We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it...

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Year 2018

• Coronas and Domination Subdivision Number of a Graph

  Publication

  • M. Dettlaff
  • M. Lemańska
  • J. Topp
  • P. Żyliński

  - Bulletin of the Malaysian Mathematical Sciences Society - Year 2018

  In this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G ◦P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.

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• Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1

  Publication

  • K. Bartoszek
  • M. Pułka

  - Bulletin of the Malaysian Mathematical Sciences Society - Year 2018

  This paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the L1 space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a dense and open set in the topology induced by a very natural metric. This shows the typical long-term behaviour of iterates of quadratic stochastic operators.

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Year 2016

• Domination-Related Parameters in Rooted Product Graphs

  Publication

  • D. Kuziak
  • M. Lemańska
  • I. G. Yero

  - Bulletin of the Malaysian Mathematical Sciences Society - Year 2016

  Abstract A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging to S. A domination parameter of G is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of G. Here, we investigate several domination-related parameters in rooted product graphs.

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• Non-isolating bondage in graphs

  Publication

  • M. Krzywkowski

  - Bulletin of the Malaysian Mathematical Sciences Society - Year 2016

  A dominating set of a graph $G = (V,E)$ is a set $D$ of vertices of $G$ such that every vertex of $V(G) \setminus D$ has a neighbor in $D$. The domination number of a graph $G$, denoted by $\gamma(G)$, is the minimum cardinality of a dominating set of $G$. The non-isolating bondage number of $G$, denoted by $b'(G)$, is the minimum cardinality among all sets of edges $E' \subseteq E$ such that $\delta(G-E') \ge 1$ and $\gamma(G-E')...

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