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Metric dimension and zero forcing number of two families of line graphs

Linda Eroh;  Cong X. Kang;  Eunjeong Yi — 2014

Mathematica Bohemica

Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the “AIM Minimum Rank–Special Graphs Work Group”, whereas metric dimension is a well-known graph parameter. We investigate the metric dimension and the zero forcing number of some line graphs by first determining the metric dimension and the zero forcing number of the line graphs of wheel graphs and the bouquet of circles. We prove that Z ( G ) ≤ 2 Z ( L ( G ) ) for a simple and connected graph G . Further,...

Domination in functigraphs

Linda Eroh;  Ralucca Gera;  Cong X. Kang;  Craig E. Larson;  Eunjeong Yi — 2012

Discussiones Mathematicae Graph Theory

Let G₁ and G₂ be disjoint copies of a graph G, and let f:V(G₁) → V(G₂) be a function. Then a functigraph C(G,f) = (V,E) has the vertex set V = V(G₁) ∪ V(G₂) and the edge set E = E(G₁) ∪ E(G₂) ∪ {uv | u ∈ V(G₁), v ∈ V(G₂),v = f(u)}. A functigraph is a generalization of a permutation graph (also known as a generalized prism) in the sense of Chartrand and Harary. In this paper, we study domination in functigraphs. Let γ(G) denote the domination number of G. It is readily seen that γ(G) ≤ γ(C(G,f))...

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