In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of dista...In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B.A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B.The dominant metric dimension of G is the cardinality number of the minimum dominant resolving set.The dominant metric dimension is computed by a binary version of the Archimedes optimization algorithm(BAOA).The objects of BAOA are binary encoded and used to represent which one of the vertices of the graph belongs to the dominant resolving set.The feasibility is enforced by repairing objects such that an additional vertex generated from vertices of G is added to B and this repairing process is iterated until B becomes the dominant resolving set.This is the first attempt to determine the dominant metric dimension problem heuristically.The proposed BAOA is compared to binary whale optimization(BWOA)and binary particle optimization(BPSO)algorithms.Computational results confirm the superiority of the BAOA for computing the dominant metric dimension.展开更多
in this paper, we present a new unidirectional graph, the 'alternating graph. Like the known (unidirectional) n-cube and (unidirectional) n-star, the alternating graph is shown to possess rich structure and symmet...in this paper, we present a new unidirectional graph, the 'alternating graph. Like the known (unidirectional) n-cube and (unidirectional) n-star, the alternating graph is shown to possess rich structure and symmetry properties as well as many desirable fault tolerant characteristics展开更多
文摘In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B.A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B.The dominant metric dimension of G is the cardinality number of the minimum dominant resolving set.The dominant metric dimension is computed by a binary version of the Archimedes optimization algorithm(BAOA).The objects of BAOA are binary encoded and used to represent which one of the vertices of the graph belongs to the dominant resolving set.The feasibility is enforced by repairing objects such that an additional vertex generated from vertices of G is added to B and this repairing process is iterated until B becomes the dominant resolving set.This is the first attempt to determine the dominant metric dimension problem heuristically.The proposed BAOA is compared to binary whale optimization(BWOA)and binary particle optimization(BPSO)algorithms.Computational results confirm the superiority of the BAOA for computing the dominant metric dimension.
基金Trans-Century Training Programme Foundation for the Talents by the StateEducation Commission.
文摘in this paper, we present a new unidirectional graph, the 'alternating graph. Like the known (unidirectional) n-cube and (unidirectional) n-star, the alternating graph is shown to possess rich structure and symmetry properties as well as many desirable fault tolerant characteristics
