We consider the problem (MSSS) of nding a strongly connected spanning subgraph with the minimum number of arcs in a strongly connected digraph. This problem is NP-hard for general digraphs since it generalizes the hamil-tonian cycle problem. We show that the problem is polynomially solvable for quasi-transitive digraphs. We describe the minimum number of arcs in such a spanning subgraph of a qu...

A fundamental problem in wireless sensor networks is to connect a given set of sensors while minimizing the receiver interference. This is modeled as follows: each sensor node corresponds to a point in R and each transmission range corresponds to a ball. The receiver interference of a sensor node is defined as the number of transmission ranges it lies in. Our goal is to choose transmission radi...

We derive strong structural constraints on the automorphism groups of strongly regular (s. r.) graphs, giving a surprisingly strong answer to a decades-old problem, with tantalizing implications to testing isomorphism of s. r. graphs, and raising new combinatorial challenges. S. r. graphs, while not believed to be Graph Isomorphism (GI) complete, have long been recognized as hard cases for GI, ...

Individuals eligible in both Medicaid and Medicare, the dually eligible enrollees, account for a disproportionate share of Medicaid utilization and payments. While comprising 14.7 percent of the Medicaid population, they accounted for 40.5 percent of Medicaid payments in 2002. Mean reimbursement for the dually eligible enrollees was nearly four times that of non-dually eligible Medicaid enrolle...

The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion a dual hemimorphism. In this paper, we focus on from logical point view. paper presents extensive investigation logic corresponding to and its axiomatic extensions, along with equally universal algebraic study their semantics. Firstly, present Hilbert-style axio...

Let C be a family of cliques of a graph G = (V,E). Suppose that each clique C of C is associated with an integer r(C), where r(C) ≥ 0. A vertex v r-dominates a clique C of G if d(v, x) ≤ r(C) for all x ∈ C, where d(v, x) is the standard graph distance. A subset D ⊆ V is a clique r-dominating set of G if for every clique C ∈ C there is a vertex u ∈ D which r-dominates C. A clique r-packing set i...