TY - GEN

T1 - On local adjacency metric dimension of some wheel related graphs with pendant points

AU - Rinurwati,

AU - Suprajitno, Herry

AU - Slamin,

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

PY - 2017/8/1

Y1 - 2017/8/1

N2 - Let G = (V(G),E(G)) be any connected graph of order n = |V(G)| and measure m = |E(G)|. For an order set of vertices S = { s1, s2, ..., sk} and a vertex v in G, the adjacency representation of v with respect to S is the ordered k-tuple rA(v|S) = (dA(v, s1), dA(v, s2), ..., dA(v, sk)), where dA(u,v) represents the adjacency distance between the vertices u and v. The set S is called a local adjacency resolving set of G if for every two distinct vertices u and v in G, u adjacent v then rA(u|S)≠rA(v|S). A minimum local adjacency resolving set for G is a local adjacency metric basis of G. Local adjacency metric dimension for G, dimA,l(G), is the cardinality of vertices in a local adjacency metric basis for G. In this paper, we study and determine the local adjacency metric dimension of some wheel related graphs G (namely gear graph, helm, sunflower and friendship graph) with pendant points, that is edge corona product of G and a trivial graph K1, G⋄K1. Moreover, we compare among the local adjacency metric dimension of G⋄K1 graph,of Wn⋄K1 graph and metric dimension of Wn.

AB - Let G = (V(G),E(G)) be any connected graph of order n = |V(G)| and measure m = |E(G)|. For an order set of vertices S = { s1, s2, ..., sk} and a vertex v in G, the adjacency representation of v with respect to S is the ordered k-tuple rA(v|S) = (dA(v, s1), dA(v, s2), ..., dA(v, sk)), where dA(u,v) represents the adjacency distance between the vertices u and v. The set S is called a local adjacency resolving set of G if for every two distinct vertices u and v in G, u adjacent v then rA(u|S)≠rA(v|S). A minimum local adjacency resolving set for G is a local adjacency metric basis of G. Local adjacency metric dimension for G, dimA,l(G), is the cardinality of vertices in a local adjacency metric basis for G. In this paper, we study and determine the local adjacency metric dimension of some wheel related graphs G (namely gear graph, helm, sunflower and friendship graph) with pendant points, that is edge corona product of G and a trivial graph K1, G⋄K1. Moreover, we compare among the local adjacency metric dimension of G⋄K1 graph,of Wn⋄K1 graph and metric dimension of Wn.

UR - http://www.scopus.com/inward/record.url?scp=85027980126&partnerID=8YFLogxK

U2 - 10.1063/1.4994468

DO - 10.1063/1.4994468

M3 - Conference contribution

AN - SCOPUS:85027980126

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 -