Abstract
In this paper we focus on the issue related to finding the resolving connected dominating sets (RCDSs) of a graph, denoted by G. The connected dominating set (CDS) is a connected subset of vertices of G selected to guarantee that all vertices in the graph are connected to vertices in the CDS. The connected dominating set with minimum cardinality, or minimum CDS (MCDS), is an adequate virtual backbone for information interchange in a network. When distinct vertices of G have also distinct representations with respect to a subset of vertices in the MCDS, it is said that the MCDS includes a resolving set (RS) of G. With this work, we explore different strategies to find the RCDS with minimum cardinality in complex networks where the vertices have different importances.
Highlights
A weighted network can be modeled as a graph where the vertices have weights representing the metric of some relevant parameter
In Ref [16], we have proposed an algorithm based on constructing the connected dominating set (CDS) for any type of graph taking into account both weights and degrees of vertices
Since the calculation of an resolving connected dominating sets (RCDSs) is an NP-complex problem, we propose to find the RCDS as the union of the resolving set (RS) and the minimum CDS (MCDS)
Summary
A weighted network can be modeled as a graph where the vertices have weights representing the metric of some relevant parameter. The identification of such relevant vertices is important for better control of disease spreading [1], design of marketing strategies [2], optimization of limited resource allocation [3], and so on. The first definitions of graph entropy were presented by Rasherky [4], Trucco [5], and Mowshowitz [6,7,8,9]. We recommend consulting the survey presented in [10]
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