TY - JOUR

T1 - The similarity of metric dimension and local metric dimension of rooted product graph

AU - Susilowati, L.

AU - Slamin,

AU - Utoyo, M. I.

AU - Estuningsih, N.

N1 - Publisher Copyright:
© 2015 Pushpa Publishing House, Allahabad, India

PY - 2015/7/2

Y1 - 2015/7/2

N2 - Let G be a connected graph with vertex set V(G) and W = {w1, w2,..., wk}⊂V(G). The representation of a vertex v∈V(G) with respect to W is the ordered k-tuple r(v |W) = (d(v, w1), d(v, w2),..., d(v, wk )), where d(v, w) represents the distance between vertices v and w. The set W is called a resolving set for G if every vertex of G has a distinct representation. A resolving set containing a minimum number of vertices is called basis for G. The metric dimension of G, denoted by dim(G), is the number of vertices in a basis of G. If every two adjacent vertices of G have a distinct representation with respect to W, then the set W is called a local resolving set for G and the minimum local resolving set is called a local basis of G. The cardinality of a local basis of G is called local metric dimension of G, denoted by diml (G). In this paper, we study the local metric dimension of rooted product graph and the similarity of metric dimension and local metric dimension of rooted product graph.

AB - Let G be a connected graph with vertex set V(G) and W = {w1, w2,..., wk}⊂V(G). The representation of a vertex v∈V(G) with respect to W is the ordered k-tuple r(v |W) = (d(v, w1), d(v, w2),..., d(v, wk )), where d(v, w) represents the distance between vertices v and w. The set W is called a resolving set for G if every vertex of G has a distinct representation. A resolving set containing a minimum number of vertices is called basis for G. The metric dimension of G, denoted by dim(G), is the number of vertices in a basis of G. If every two adjacent vertices of G have a distinct representation with respect to W, then the set W is called a local resolving set for G and the minimum local resolving set is called a local basis of G. The cardinality of a local basis of G is called local metric dimension of G, denoted by diml (G). In this paper, we study the local metric dimension of rooted product graph and the similarity of metric dimension and local metric dimension of rooted product graph.

KW - Basis

KW - Local basis

KW - Local resolving set

KW - Resolving set

KW - Rooted product graph

UR - http://www.scopus.com/inward/record.url?scp=84934780396&partnerID=8YFLogxK

U2 - 10.17654/FJMSAug2015_841_856

DO - 10.17654/FJMSAug2015_841_856

M3 - Article

AN - SCOPUS:84934780396

SN - 0972-0871

VL - 97

SP - 841

EP - 856

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

IS - 7

ER -