We find a lower bound for the k-subdomination number on set of graphs with given upper vertex degrees. study cases where proposed is sharp, construct optimal and indicate corresponding k-subdominating functions. The results are interpreted in terms social structures.

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.

This thesis deals with degree-constrained graph modification problems. In particular, we investigate the computational complexity of DAG Realization and Degree Anonymity. The DAG Realization problem is, given a multiset of positive integer pairs, to decide whether there is a realizing directed acyclic graph (DAG), that is, pairs are one-to-one assigned to vertices such that the indegree and the...

Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...