Please use this identifier to cite or link to this item: https://repository.unej.ac.id/xmlui/handle/123456789/92349
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dc.contributor.authorAlfarisi, Ridho-
dc.contributor.authorDafik, Dafik-
dc.contributor.authorKristiana, Arika Indah-
dc.contributor.authorAgustin, Ika Hesti-
dc.date.accessioned2019-09-02T03:18:50Z-
dc.date.available2019-09-02T03:18:50Z-
dc.date.issued2019-09-02-
dc.identifier.issn2227-524X-
dc.identifier.urihttp://repository.unej.ac.id/handle/123456789/92349-
dc.descriptionInternational Journal of Engineering &Technology, 8 (3) (2019) 120-124en_US
dc.description.abstractAll graphs in this paper are nontrivial and connected graph. For 𝑘-ordered set 𝑊 = {𝑠1, 𝑠2, … , 𝑠𝑘} of vertex set 𝐺, the multiset representation of a vertex 𝑣 of 𝐺 with respect to 𝑊 is 𝑟𝑚(𝑣|𝑊) = {𝑑(𝑣, 𝑠1), 𝑑(𝑣, 𝑠2), … , 𝑑(𝑣, 𝑠𝑘)} where 𝑑(𝑣, 𝑠𝑖) is a distance between of the vertex 𝑣 and the vertices in 𝑊 together with their multiplicities. The resolving set 𝑊 is a local resolving set of 𝐺 if𝑟𝑚(𝑣|𝑊) ≠ 𝑟𝑚(𝑢|𝑊) for every pair 𝑢, 𝑣 of adjacent vertices of 𝐺. The minimum local resolving set 𝑊 is a local multiset basis of 𝐺. If 𝐺 has a local multiset basis, then its cardinality is called local multiset dimension,denoted by 𝜇𝑙(𝐺). If 𝐺 does not contain a local resolving set, then we write 𝜇𝑙(𝐺) = ∞. In our paper, we will investigate the establish sharp bounds of the local multiset dimension of 𝐺 and determine the exact value of some family graphs.en_US
dc.language.isoenen_US
dc.subjectLocal Resolving Seten_US
dc.subjectLocal Multiset Dimensionen_US
dc.subjectDistanceen_US
dc.subjectSome Family Graphen_US
dc.titleThe Local Multiset Dimension of Graphsen_US
dc.typeArticleen_US
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