Year 2019

• Decontaminating Arbitrary Graphs by Mobile Agents: a Survey

  Publication

  • D. Osula

  - UTILITAS MATHEMATICA - Year 2019

  A team of mobile agents starting from homebases need to visit and clean all nodes of the network. The goal is to find a strategy, which would be optimal in the sense of the number of needed entities, the number of moves performed by them or the completion time of the strategy. Currently, the field of distributed graph searching by a team of mobile agents is rapidly expanding and many new approaches and models are being presented...

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Year 2015

• On trees with equal domination and total outer-independent domination numbers

  Publication

  • M. Krzywkowski

  - UTILITAS MATHEMATICA - Year 2015

  For a graph G=(V,E), a subset D subseteq V(G) is a dominating set if every vertex of V(G)D has a neighbor in D, while it is a total outer-independent dominating set if every vertex of G has a neighbor in D, and the set V(G)D is independent. The domination (total outer-independent domination, respectively) number of G is the minimum cardinality of a dominating (total outer-independent dominating, respectively) set of G. We characterize...

Year 2012

• On the double bondage in graphs

  Publication

  • M. Krzywkowski

  - UTILITAS MATHEMATICA - Year 2012

  A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G, denoted by gamma_d(G), is the minimum cardinality of a double dominating set of G. The double bondage number of G, denoted by b_d(G), is the minimum cardinality among all sets...