TY - GEN

T1 - Local metric dimension of circulant graph c i r c (n: 1, 2, ..., n + 1 2)

AU - Rimadhany, Ruzika

AU - Darmaji, D.

N1 - Publisher Copyright:
© 2017 Author(s).

PY - 2017/8/1

Y1 - 2017/8/1

N2 - Let G be a connected graph with two vertices u and v. The distance between u and v, denoted by d(u, v), is defined as length of the shortest path from u to v in G. For an ordered set W = {w1, w2, w3, ..., wk} of k distinct vertices in a nontrivial connected graph G, the representation of a vertex v of V(G) respect to W is r(v|W) = (d(v, w1), d(v, w2), ..., d(v, wk)). The set W is a resolving set of G if r(v|W) for each vertex v ∈ V(G) is distinct. A resolving set of minimum cardinality is a metric dimension and denoted by dim(G). The set W is a local resolving set of G if r(v|W) for every two adjacent vertices of V(G) is distinct. The minimum cardinality of local resolving set of G is a local metric dimension and denoted by ldim(G). In this research, we determine local metric dimension of circulant graph circ(n:1,2,3,...,n+12).

AB - Let G be a connected graph with two vertices u and v. The distance between u and v, denoted by d(u, v), is defined as length of the shortest path from u to v in G. For an ordered set W = {w1, w2, w3, ..., wk} of k distinct vertices in a nontrivial connected graph G, the representation of a vertex v of V(G) respect to W is r(v|W) = (d(v, w1), d(v, w2), ..., d(v, wk)). The set W is a resolving set of G if r(v|W) for each vertex v ∈ V(G) is distinct. A resolving set of minimum cardinality is a metric dimension and denoted by dim(G). The set W is a local resolving set of G if r(v|W) for every two adjacent vertices of V(G) is distinct. The minimum cardinality of local resolving set of G is a local metric dimension and denoted by ldim(G). In this research, we determine local metric dimension of circulant graph circ(n:1,2,3,...,n+12).

UR - http://www.scopus.com/inward/record.url?scp=85028015548&partnerID=8YFLogxK

U2 - 10.1063/1.4994456

DO - 10.1063/1.4994456

M3 - Conference contribution

AN - SCOPUS:85028015548

T3 - AIP Conference Proceedings

BT - International Conference on Mathematics - Pure, Applied and Computation

A2 - Adzkiya, Dieky

PB - American Institute of Physics Inc.

T2 - 2nd International Conference on Mathematics - Pure, Applied and Computation: Empowering Engineering using Mathematics, ICoMPAC 2016

Y2 - 23 November 2016

ER -