Given a simple graph G = (V, E) and a fixed positive integer k. In a graph G, a vertex is said to dominate itself and all of its neighbors. A set D ⊆ V is called a k-tuple dominating set if every vertex in V is dominated by at least k vertices of D. The k-tuple domination problem is to find a minimum cardinality k-tuple dominating set. This problem is NP-complete for general graphs. In this pap...

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure and its numerous applications. Several efficient algorithms for optimization problems that are NP-hard on general graphs have been designed for tolerance grap...

Trapezoid graphs are the intersection family of trapezoids where every trapezoid has a pair of opposite sides lying on two parallel lines. These graphs have received considerable attention and lie strictly between permutation graphs (where the trapezoids are lines) and cocomparability graphs (the complement has a transitive orientation). The operation of “vertex splitting”, introduced in [3], f...

Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance "Minimum Weighted Dominating Set" (MWDS) problem can be solved in O∗(23k) time given a boolean-decomposition of width k, hence for all graph classes where a boolean-decomposition of width O(log n) can be found in polynomial time, MWDS can be solved...

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This class of graphs has been extensively studied, due to both its interesting structure and its numerous applications (in bioinformatics, constrained-based temporal reasoning, resource allocation, and scheduling problems, among others). Several efficient al...

Reliability of networks is an important issue in the field of graph and network. Computation of network vulnerability parameters is NP-complete for popular network topologies such as tree, Mesh, Cube, etc.In this paper, we will show that the tenacity and rupture degree parameters for trapezoid graphs can be computed in polynomial time.