• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.193-204
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• 2022

A subset S of V(G), where G is a simple undirected graph, is a hop dominating set if for each v ∈ V(G)＼S, there exists w ∈ S such that d_G(v, w) = 2 and it is a locating-hop set if N_G(v, 2) ∩ S ≠ N_G(v, 2) ∩ S for any two distinct vertices u, v ∈ V(G)＼S. A set S ⊆ V(G) is a locating-hop dominating set if it is both a locating-hop and a hop dominating set of G. The minimum cardinality of a locating-hop dominating set of G, denoted by 𝛄_lh(G), is called the locating-hop domination number of G. In this paper, we investigate some properties of this newly defined parameter. In particular, we characterize the locating-hop dominating sets in graphs under some binary operations.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.4
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• pp.1661-1678
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• 2016

Clustering is one of the key technologies in vehicular networks. Constructing and maintaining stable clusters is a challenging task in high mobility environments. DWCM (Distributed and Weighted Clustering based on Mobility Metrics) is proposed in this paper based on the d-hop dominating set of the network. Each vehicle is assigned a priority that describes the cluster relationship. The cluster structure is determined according to the d-hop dominating set, where the vehicles in the d-hop dominating set act as the cluster head nodes. In addition, cluster maintenance handles the cluster structure changes caused by node mobility. The rationality of the proposed algorithm is proven. Simulation results in the NS-2 and VanetMobiSim integrated environment demonstrate the performance advantages.