Search results for: ITALIAN DOMINATION

• Secure Italian domination in graphs

  Publication

  • M. Dettlaff
  • M. Lemańska
  • J. A. RODRíGUEZ-VELáZQUEZ

  - JOURNAL OF COMBINATORIAL OPTIMIZATION - Year 2021

  An Italian dominating function (IDF) on a graph G is a function f:V(G)→{0,1,2} such that for every vertex v with f(v)=0, the total weight of f assigned to the neighbours of v is at least two, i.e., ∑u∈NG(v)f(u)≥2. For any function f:V(G)→{0,1,2} and any pair of adjacent vertices with f(v)=0 and u with f(u)>0, the function fu→v is defined by fu→v(v)=1, fu→v(u)=f(u)−1 and fu→v(x)=f(x) whenever x∈V(G)∖{u,v}. A secure Italian dominating...

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