Search results for: DOMINATION IN GRAPHS

• On proper (1,2)‐dominating sets in graphs

  Publication

  • A. Michalski
  • I. Włoch
  • M. Dettlaff
  • M. Lemańska

  - MATHEMATICAL METHODS IN THE APPLIED SCIENCES - Year 2022

  In 2008, Hedetniemi et al. introduced the concept of (1,)-domination and obtained some interesting results for (1,2) -domination. Obviously every (1,1) -dominating set of a graph (known as 2-dominating set) is (1,2) -dominating; to distinguish these concepts, we define a proper (1,2) -dominating set of a graph as follows: a subset is a proper (1,2) -dominating set of a graph if is (1,2) -dominating and it is not a (1,1) -dominating...

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• Super Dominating Sets in Graphs

  Publication

  • M. Lemańska
  • V. Swaminathan
  • Y. Venkatakrishnan
  • R. Zuazua

  - PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES - Year 2015

  In this paper some results on the super domination number are obtained. We prove that if T is a tree with at least three vertices, then n2≤γsp(T)≤n−s, where s is the number of support vertices in T and we characterize the extremal trees.

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• INFLUENCE OF A VERTEX REMOVING ON THE CONNECTED DOMINATION NUMBER – APPLICATION TO AD-HOC WIRELESS NETWORKS

  Publication

  • M. Dettlaff
  • M. Lemańska
  • A. Dapena
  • M. J. Souto-Salorio

  - Year 2015

  A minimum connected dominating set (MCDS) can be used as virtual backbone in ad-hoc wireless networks for efficient routing and broadcasting tasks. To find the MCDS is an NP- complete problem even in unit disk graphs. Many suboptimal algorithms are reported in the literature to find the MCDS using local information instead to use global network knowledge, achieving an important reduction in complexity. Since a wireless network...

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