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For a nontrivial connected graph G, let c : V (G) → N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) = NC(v) for every pair u, v of adjacent vertices of G. The minimum number of colors… (More)

The competition graph of a loopless symmetric digraph If is the rwo-.\rc'p grclph. S,(H). Necessary and sufficient conditions on If are given for S,(ff) to be interval or unit interval. These are useful properties when application requires that the competition graph be efficiently colorable. Computational aspects are discussed. as are related open problems.… (More)

Competition graphs were rst introduced by Joel Cohen in the study of food webs and have since been extensively studied. Graphs which are the competition graph of a strongly connected or Hamiltonian digraph are of particular interest in applications to communication networks. It has been previously established that every graph without isolated vertices… (More)

Large complex systems need to be analysed prior to operation so that those depending upon them for the protection of their information have a well defined understanding of the measures that have been taken to achieve security and the residual risk the system owner assumes during its operation. The U.S. military calls this analysis and vetting process… (More)

- Ralucca Gera, Craig Rasmussen, Pantelimon St˘ Anic, Steve Horton
- 2006

Let G be a graph with the vertex set V (G), edge set E(G). A vertex labeling is a bijection f : V (G) → {1, 2,. .. , |V (G)|}. The weight of e = uv ∈ E(G) is given by g(e) = min{f (u), f (v)}. The min-sum vertex cover (msvc) is a vertex labeling that minimizes the vertex cover number µ s (G) = e∈E(G) g(e). The minimum such sum is called the msvc cost. In… (More)

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