Please use this identifier to cite or link to this item: https://ir.swu.ac.th/jspui/handle/123456789/27563
ชื่อเรื่อง: Graph Realizations Constrained by Connected Local Dimensions and Connected Local Bases
ผู้แต่ง: Khemmani V.
Pho-On W.
Isariyapalakul S.
วันที่เผยแพร่: 2022
บทคัดย่อ: For an ordered set W = {w1, w2, ⋯, wk} of k distinct vertices in a connected graph G, the representation of a vertex v of G with respect to W is the k-vector r(v|W) = (d(v,w1), d(v,w2), ⋯, d(v,wk)), where d(v,wi) is the distance from v to wifor 1 ≤ i ≤ k. The setW is called a connected local resolving set of G if the representations of every two adjacent vertices of G with respect to W are distinct and the subgraph 〈W〉 induced by W is connected. A connected local resolving set of G of minimum cardinality is a connected local basis of G. The connected local dimension cld(G) of G is the cardinality of a connected local basis of G. In this paper, the connected local dimensions of some well-known graphs are determined. We study the relationship between connected local bases and local bases in a connected graph, and also present some realization results. © 2022 World Scientific and Engineering Academy and Society. All rights reserved.
URI: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85122803134&doi=10.37394%2f23206.2022.21.1&partnerID=40&md5=9f583fdc14f587394206b994813bf400
https://ir.swu.ac.th/jspui/handle/123456789/27563
ISSN: 11092769
Appears in Collections:Scopus 2022

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