## Abstract

Let G be a connected graph. The distance between two vertices u and v in G, denoted by d_{G}(u,v), is the number of edges in a shortest path from u to v, while the distance between an edge e=xy and a vertex v in G is d_{G}(e,v)=min{d_{G}(x,v),d_{G}(y,v)}. For an edge e∈E(G) and a subset S of V(G), the representation of e with respect to S={x_{1},…,x_{k}} is the vector r_{G}(e|S)=(d_{1},…,d_{k}), where d_{i}=d_{G}(e,x_{i}) for i∈[k]. If r_{G}(e|S)≠r_{G}(f|S) for every two adjacent edges e and f of G, then S is called a local edge metric generator for G. The local edge metric dimension of G, denoted by edim_{ℓ}(G), is the minimum cardinality among all local edge metric generators in G. For two non-trivial graphs G and H, we determine edim_{ℓ}(G⋄H) in the edge corona product G⋄H and we determine edim_{ℓ}(G∘H) in the corona product G⋄H. We also formulate the problem of computing edim_{ℓ}(G) as an integer linear programming model.

Original language | English |
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Article number | 358 |

Journal | Computational and Applied Mathematics |

Volume | 43 |

Issue number | 6 |

DOIs | |

Publication status | Published - Sept 2024 |

## Keywords

- 05C12
- 05C76
- Corona product
- Edge corona product
- Integer linear programming
- Local edge metric dimension
- Metric dimension

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics