Publication:
Graph Realizations Constrained by Connected Local Dimensions and Connected Local Bases

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Issued Date

2022

Resource Type

Article

Language

eng

File Type

application/pdf

ISSN

11092769

DOI

10.37394/23206.2022.21.1

Rights Holder(s)

Scopus

Bibliographic Citation

WSEAS Transactions on Mathematics. Vol 21, No. (2022), p.1-8

Suggested Citation

Khemmani V., Pho-On W., Isariyapalakul S. Graph Realizations Constrained by Connected Local Dimensions and Connected Local Bases. WSEAS Transactions on Mathematics. Vol 21, No. (2022), p.1-8. doi:10.37394/23206.2022.21.1 Retrieved from: https://hdl.handle.net/20.500.14740/10310

Title

Graph Realizations Constrained by Connected Local Dimensions and Connected Local Bases

Author(s)

Khemmani V.
 Pho-On W.
 Isariyapalakul S.

Abstract

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.

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URI

https://hdl.handle.net/20.500.14740/10310

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Scopus: Year 2022

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