## Abstract

An ordered set of vertices S is called as a (local) resolving set of a connected graph G = (V_{G}, E_{G}) if for any two adjacent vertices s ≠ t ∈ V_{G} have distinct representation with respect to S, that is r(s | S) ≠ r(t | S). A representation of a vertex in G is a vector of distances to vertices in S. The minimum (local) resolving set for G is called as a (local) basis of G. A (local) metric dimension for G denoted by dim(G), is the cardinality of vertices in a basis for G, and its local variant by dim_{l} (G). Given two graphs, G with vertices s_{1}, s_{2}, ⋯, s_{p} and edges e_{1}, e_{2}, ⋯, e_{q} , and H. An edge-corona of G and H, G⋄H is defined as a graph obtained by taking a copy of G and q copies of H and for each edge e_{j} = s_{i}s_{h} of G joining edges between the two end-vertices s_{i}, s_{h} of e_{j} and each vertex of j-copy of H. In this paper, we determine and compare between the metric dimension of graphs with m-pendant points, G⋄mK_{1}, and its local variant for any connected graph G. We give an upper bound of the dimensions.

Original language | English |
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Article number | 012035 |

Journal | Journal of Physics: Conference Series |

Volume | 855 |

Issue number | 1 |

DOIs | |

Publication status | Published - 12 Jun 2017 |

Event | 1st International Conference on Mathematics: Education, Theory, and Application, ICMETA 2016 - Surakarta, Indonesia Duration: 6 Dec 2016 → 7 Dec 2016 |