Spanning k-ended trees of 3-regular connected graphs

Hamed Ghasemian Zoeram (Faculty of Agriculture and Animal Science, University of Torbat-e Jam, Iran)
Daniel Yaqubi (Faculty of Agriculture and Animal Science, University of Torbat-e Jam, Iran)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 5, No 2 (2017): Electronic Journal of Graph Theory and Applications

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 $|End(T)| \leq k$. 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.