Open AccessMetric and edge-metric dimensions of bobble-neighbourhood-corona graphs
Author(s) -
Rinurwati,
Roida Nabila
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1836/1/012010
Subject(s) - neighbourhood (mathematics) , combinatorics , metric dimension , mathematics , vertex (graph theory) , graph , discrete mathematics , cardinality (data modeling) , metric (unit) , line graph , computer science , mathematical analysis , 1 planar graph , operations management , economics , data mining
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 H i with H i 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 K 1 , and G £ {C n ,K n }.