Weak Vertex Cover Problem in Certain Non-Regular Graphs

Graphs are used to represent network topologies where a processor is considered as a vertex and a communication link between processors as an edge between corresponding vertices. A beneficial method of monitoring the network flow is obtaining a flow monitoring set which consists of smallest amount of nodes of a graph G. The smallest flow monitoring set problem for an underlying network can be solved by reducing it to the weak vertex cover (WVC) problem of G, which is NP-hard. This paper deals with the weak cover concept of certain graph classes. Our results indicate that our work is valuable to solve weak vertex cover problem which can be applied in network management and in security of IoT services. (C) 2018 The Authors. Published by Elsevier B.V.