摘要

The independent vertex edge domination number and the upper non-enclaving number of a graph G are denoted by i(ve)(G) and Psi(G), respectively. Boutrig et al. posed the following question: Let G be a connected graph with order n. Is Psi(G)-i(ve)(G) <= n? In this paper, we provide an infinite family of counterexamples. A new relationship between Psi(G) and i(ve)(G) is established. Furthermore, if G is a connected cubic graph, we answer this question in the affirmative.