An ordered set of vertices S is called as a (local) resolving set of a connected graph G = (VG, EG) if for any two adjacent vertices s ≠ t ∈ VG 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 diml (G). Given two graphs, G with vertices s1, s2, ⋯, sp and edges e1, e2, ⋯, eq , 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 ej = sish of G joining edges between the two end-vertices si, sh of ej 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⋄mK1, and its local variant for any connected graph G. We give an upper bound of the dimensions.
|Journal||Journal of Physics: Conference Series|
|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