This article investigates numerous integer sequences derived from two special balanced k-ary trees. Main contributions of this article are two fold. The first one is building a taxonomy of various balanced trees. The other pertains to discovering new integer sequences and generalizing existing integer sequences to balanced k-ary trees. The generalized integer sequence formulae for the sum of he...

The problem of constructing the suffix tree of a tree is a generalization of the problem of constructing the suffix tree of a string. It has many applications, such as in minimizing the size of sequential transducers and in tree pattern matching. The best-known algorithm for this problem is Breslauer’s O(n log |Σ|) time algorithm where n is the size of the CS-tree and |Σ| is the alphabet size, ...

for two given graphs g1 and g2, the ramseynumber r(g1,g2) is the smallest integer n such that for anygraph g of order n, either $g$ contains g1 or the complementof g contains g2. let tn denote a tree of order n andwm a wheel of order m+1. to the best of our knowledge, only r(tn,wm) with small wheels are known.in this paper, we show that r(tn,wm)=3n-2 for odd m with n>756m^{10}.

For an integer k with k ≥ 2, a k-tree (resp. a k-forest) is a tree (resp. forest) with maximum degree at most k. In this paper, we show that for any integer k with k ≥ 3, any connected K1,k+1-free graph has a spanning k-tree or a spanning k-forest with only large components.

Discovering new integer sequences and generalizing the existing ones are important and of great interest. In this article, various balanced k-ary trees are first studied and their taxonomy is built. In particular, two systematic balanced k-ary trees, whose nth tree is determined by a certain algorithm, are identified, i.e., complete and sizebalanced k-ary trees. The integer sequences from the f...