TY - GEN

T1 - The complement edge metric dimension of graphs

AU - Rosyidah, Nirmala Mega

AU - Rinurwati,

N1 - Publisher Copyright:
© 2022 Author(s).

PY - 2022/12/19

Y1 - 2022/12/19

N2 - In this paper, we construct the new concept namely the complement edge metric dimension on the graph, which is the result of combining two concepts. The first concept is edge metric dimension and in the second concept is complement metric dimension. Let given a graph G=(V(G), E(G)) where V(G) = {v1, v2, ..., vn} and also a set M = {m1, ..., mk} ⊂ V(G) that indicate connected graph and an ordered set, respectively. The representation of the edge e=xy∈E(G) with respect to M can be written as r(e|M) = (d(e, mi))=(min{d(x, mi), d(y, mi)}) where d(x, mi) and d(y, mi) indicate the distance from vertex x to mi and from vertex y to mi for i∈{1,2, ..., k}, respectively. The definition of a complement edge resolving set of G is if any two distinct edges in G have the same representation with respect to M. If set M has maximum cardinality then it is called a complement edge basis. Next, the number of vertices of M is called the complement edge metric dimension of G that can be written as edim¯(G). As a result, the complement edge metric dimension which is implemented in basic graphs, namely graph Pn, graph Sn, graph Cn, and graph Kn will be determined.

AB - In this paper, we construct the new concept namely the complement edge metric dimension on the graph, which is the result of combining two concepts. The first concept is edge metric dimension and in the second concept is complement metric dimension. Let given a graph G=(V(G), E(G)) where V(G) = {v1, v2, ..., vn} and also a set M = {m1, ..., mk} ⊂ V(G) that indicate connected graph and an ordered set, respectively. The representation of the edge e=xy∈E(G) with respect to M can be written as r(e|M) = (d(e, mi))=(min{d(x, mi), d(y, mi)}) where d(x, mi) and d(y, mi) indicate the distance from vertex x to mi and from vertex y to mi for i∈{1,2, ..., k}, respectively. The definition of a complement edge resolving set of G is if any two distinct edges in G have the same representation with respect to M. If set M has maximum cardinality then it is called a complement edge basis. Next, the number of vertices of M is called the complement edge metric dimension of G that can be written as edim¯(G). As a result, the complement edge metric dimension which is implemented in basic graphs, namely graph Pn, graph Sn, graph Cn, and graph Kn will be determined.

UR - http://www.scopus.com/inward/record.url?scp=85145467228&partnerID=8YFLogxK

U2 - 10.1063/5.0131823

DO - 10.1063/5.0131823

M3 - Conference contribution

AN - SCOPUS:85145467228

T3 - AIP Conference Proceedings

BT - 7th International Conference on Mathematics - Pure, Applied and Computation

A2 - Mufid, Muhammad Syifa�ul

A2 - Adzkiya, Dieky

PB - American Institute of Physics Inc.

T2 - 7th International Conference on Mathematics: Pure, Applied and Computation: , ICoMPAC 2021

Y2 - 2 October 2021

ER -