TY - JOUR

T1 - Metric and edge-metric dimensions of bobble-neighbourhood-corona graphs

AU - Rinurwati,

AU - Nabila, R. E.

N1 - Publisher Copyright:
© 2021 Published under licence by IOP Publishing Ltd.

PY - 2021/3/23

Y1 - 2021/3/23

N2 - Resolving set in a graphG =(V(G), E(G)) is an ordered subset W of V(G) such that every vertex in V(G) has distinct representation with respect to W. Resolving set of G of minimum cardinality is called basis of G.Cardinality of basis of G is called metric dimension of G, dim(G). An ordered set W is called edge resolving set of G if every edge in E(G) has distinct edge-representation with respect to W. Edge-resolving sets in a graph Gof minimum cardinality is called edge-metric basis of G. Cardinality of edge-basis of G is called as edge-metric dimension of G, edim(G). Neighbourhood corona of G and H, G*H, is agraph obtained by taking graph G and |V (G)| graph Hi with Hi i = 1,2,..., |7(G)| is copy of H, then all vertices in H are connected with neighbouring vertex of vertex v in V (G). In this paper, we determine and analyse metric and edge-metric dimension of bobble-neighbourhood-corona, that is metric and edge-metric dimension of neighbourhood-corona of G and H, G*H, with H is trivial graph K1, and G ? {Cn,Kn}.

AB - Resolving set in a graphG =(V(G), E(G)) is an ordered subset W of V(G) such that every vertex in V(G) has distinct representation with respect to W. Resolving set of G of minimum cardinality is called basis of G.Cardinality of basis of G is called metric dimension of G, dim(G). An ordered set W is called edge resolving set of G if every edge in E(G) has distinct edge-representation with respect to W. Edge-resolving sets in a graph Gof minimum cardinality is called edge-metric basis of G. Cardinality of edge-basis of G is called as edge-metric dimension of G, edim(G). Neighbourhood corona of G and H, G*H, is agraph obtained by taking graph G and |V (G)| graph Hi with Hi i = 1,2,..., |7(G)| is copy of H, then all vertices in H are connected with neighbouring vertex of vertex v in V (G). In this paper, we determine and analyse metric and edge-metric dimension of bobble-neighbourhood-corona, that is metric and edge-metric dimension of neighbourhood-corona of G and H, G*H, with H is trivial graph K1, and G ? {Cn,Kn}.

UR - http://www.scopus.com/inward/record.url?scp=85103543008&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1836/1/012010

DO - 10.1088/1742-6596/1836/1/012010

M3 - Conference article

AN - SCOPUS:85103543008

SN - 1742-6588

VL - 1836

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012010

T2 - 4th International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2020

Y2 - 22 August 2020 through 23 August 2020

ER -