University of KashanMathematics Interdisciplinary Research2538-36393120180601On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges67746351110.22052/mir.2018.115910.1087ENAbbasSeifyDepartment of Sciences,
Shahid Rajaei Teacher Training University,
Tehran, I. R. IranJournal Article20180118A tree containing exactly two non-pendant vertices is called a double-star. Let k<sub>1</sub> and k<sub>2</sub> be two positive integers. The double-star with degree sequence (k<sub>1</sub>+1, k<sub>2</sub>+1, 1, ..., 1) is denoted by S<sub>k1</sub>, <sub>k2</sub>. It is known that a cubic graph has an S<sub>1,1</sub>-decomposition if and only if it contains a perfect matching. In this paper, we study the S<sub>1,2</sub>-decomposition of cubic graphs. We present some necessary and some sufficient conditions for the existence of an S<sub>1,2</sub>-decomposition in cubic graphs.https://mir.kashanu.ac.ir/article_63511_00671cbdab52608c7230f8055860c91a.pdf