TY - JOUR

T1 - Edge metric dimensions of neighbourhood corona graph containing dominant vertices

AU - Rosyidah, N. M.

AU - Rinurwati,

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

PY - 2021/3/29

Y1 - 2021/3/29

N2 - Connected graph G = (V(G), E(G)) with V(G) = {?1, ?2,..? n } and a graph H and an ordered set Z = {z 1,z 2,...,z k} V( G) are given. The set Z, for which the representations of every two distinct edges e1, e2E (G) with respect to Z are distinct, is called edge resolving set. The edge resolving set with minimum cardinality is called edge metric basis for G, its cardinality is called edge metric dimension of G, and is denoted by e d im( G). Let H 1, H 2,...,H n be copies of graph H. The neighbourhood corona between G and H, G*H, is obtained by taking G and |V(G)| copies of H, then making all vertices in the ith copy of H adjacent to all neighbours of v i V(G), with i { 1, 2,...,n}. In this paper, we determine and analyze edge metric dimensions of neighbourhood corona between G and H, edim(G*H), where G is a graph containing dominant vertices, that is G {K n , S n , F n , W n } and is graph k 1.

AB - Connected graph G = (V(G), E(G)) with V(G) = {?1, ?2,..? n } and a graph H and an ordered set Z = {z 1,z 2,...,z k} V( G) are given. The set Z, for which the representations of every two distinct edges e1, e2E (G) with respect to Z are distinct, is called edge resolving set. The edge resolving set with minimum cardinality is called edge metric basis for G, its cardinality is called edge metric dimension of G, and is denoted by e d im( G). Let H 1, H 2,...,H n be copies of graph H. The neighbourhood corona between G and H, G*H, is obtained by taking G and |V(G)| copies of H, then making all vertices in the ith copy of H adjacent to all neighbours of v i V(G), with i { 1, 2,...,n}. In this paper, we determine and analyze edge metric dimensions of neighbourhood corona between G and H, edim(G*H), where G is a graph containing dominant vertices, that is G {K n , S n , F n , W n } and is graph k 1.

UR - http://www.scopus.com/inward/record.url?scp=85103873633&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1821/1/012017

DO - 10.1088/1742-6596/1821/1/012017

M3 - Conference article

AN - SCOPUS:85103873633

SN - 1742-6588

VL - 1821

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012017

T2 - 6th International Conference on Mathematics: Pure, Applied and Computation, ICOMPAC 2020

Y2 - 24 October 2020

ER -