Spanning k-ended trees of 3-regular connected graphs - Hamed Ghasemian Zoeram; Daniel Yaqubi (Electronic Journal of Graph Theory and Applications (EJGTA), 2017)
A vertex of degree one is called an end-vertex and the set of end-vertices of G is denoted by End(G). For a positive integer k, a tree T be called k-ended tree if $|End(T)| ≤ k$. In this paper, we obtain sufficient conditions for spanning k-trees of 3-regular connected graphs. We give a construction sequence of graphs satisfying the condition. At the end, we present a conjecture about spanning k-ended trees of 3-regular connected graphs.