ON METRIC DIMENSION OF FUNCTIGRAPHS Academic Article

abstract

• The metric dimension of a graph G, denoted by dim (G), is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let G1and G2be disjoint copies of a graph G and let f : V(G1) V(G2) be a function. Then a functigraphC(G, f) = (V, E) has the vertex set V = V(G1) V(G2) and the edge set E = E(G1) E(G2) {uv | v = f(u)}. We study how metric dimension behaves in passing from G to C(G, f) by first showing that 2 dim (C(G, f)) 2n - 3, if G is a connected graph of order n 3 and f is any function. We further investigate the metric dimension of functigraphs on complete graphs and on cycles.

authors

• Kang, Cong
• Yi, Eunjeong

published proceedings

• DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS

author list (cited authors)

• Eroh, L., Kang, C. X., & Yi, E.

citation count

• 2

complete list of authors

• Eroh, Linda||Kang, Cong X||Yi, Eunjeong

publication date

• December 2013

publisher

• World Scientific Publishing  Publisher

published in

• Discrete Mathematics, Algorithms and Applications  Journal

keywords

• Complete Graph
• Cycle
• Distance
• Functigraph
• Metric Dimension
• Resolving Set

Digital Object Identifier (DOI)

• 10.1142/S1793830912500607

start page

• 1250060

end page

• 1250060

volume

• 5

issue

• 4

URL

• http://dx.doi.org/10.1142/s1793830912500607