On double-star decomposition of graphs

On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges‎

‎A tree containing exactly two non-pendant vertices is called a double-star‎. ‎Let $k_1$ and $k_2$ be two positive integers‎. ‎The double-star with degree sequence $(k_1+1‎, ‎k_2+1‎, ‎1‎, ‎ldots‎, ‎1)$ is denoted by $S_{k_1‎, ‎k_2}$‎. ‎It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching‎. ‎In this paper‎, ‎we study the $S_{1,2}$-decomposit...

Decomposition of odd-hole-free graphs by double star cutsets and 2-joins

Peg solitaire on the windmill and the double star graphs

In a recent work by Beeler and Hoilman, the game of peg solitaire is generalized to arbitrary boards. These boards are treated as graphs in the combinatorial sense. In this paper, we extend this study by considering the windmill and the double star. Simple necessary and sufficient conditions are given for the solvability of each graph. We also discuss an open problem concerning the range of val...

On Star Coloring of Graphs

In this paper, we deal with the notion of star coloring of graphs. A star coloring of an undirected graph G is a proper vertex coloring of G (i.e., no two neighbors are assigned the same color) such that any path of length 3 in G is not bicolored. We give the exact value of the star chromatic number of different families of graphs such as trees, cycles, complete bipartite graphs, outerplanar gr...

The spectrum of the hyper-star graphs and their line graphs

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...