Upper and lower bounds on the total domination number of the direct product of graphs are given. The bounds involve the {2}-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The dom...

We investigate two problems concerning the complexity of evaluating a function f at a k-tuple of unrelated inputs by k parallel decision tree algorithms. In the product problem, for some xed depth bound d, we seek to maximize the fraction of input k-tuples for which all k decision trees are correct. Assume that for a single input to f, the best decision tree algorithm of depth d is correct on a...

Clustering is the procedure to group similar objects together. Several algorithms have been proposed for clustering. Among them, the K-means clustering method has less time complexity. But it is sensitive to extreme values and would cause less accurate clustering of the dataset. However, K-medoids method does not have such limitations. But this method uses user-defined value for K. Therefore, i...

given a graph $g$, the total dominator coloring problem seeks aproper coloring of $g$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. weseek to minimize the number of color classes. we initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. we also compare the totaldominator chro...

Let k = (k1, k2, · · · , kt) be a t-tuple of integers, and m be a positive integer. For a subset A ⊂ Zm and any n ∈ Zm, let rk A(n) denote the number of solutions of the equation k1a1 + · · ·+ ktat = n with a1, · · · , at ∈ A. In this paper, we give a necessary and sufficient condition on (k,m) such that there exists a subset A ⊂ Zm satisifying rk A = r k Zm\A. This settles a problem of Yang an...

Upper and lower bounds on the total domination number of the direct product of graphs are given. The bounds involve the {2}-total domination number and the total 2-tuple domination number of the factors. Using these relationships some exact total domination numbers are obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direc...

BACKGROUND The comparison of samples, or beta diversity, is one of the essential problems in ecological studies. Next generation sequencing (NGS) technologies make it possible to obtain large amounts of metagenomic and metatranscriptomic short read sequences across many microbial communities. De novo assembly of the short reads can be especially challenging because the number of genomes and the...

A k-extended Skolem-type 5-tuple difference set of order t is a set of t 5-tuples {(di,1, di,2, di,3, di,4, di,5) | i = 1, 2, . . . , t} such that di,1+di,2+di,3+di,4+di,5 = 0 for 1 ≤ i ≤ t and {|di,j| | 1 ≤ i ≤ t, 1 ≤ j ≤ 5} = {1, 2, . . . , 5t+1}\{k}. In this talk, we will give necessary and sufficient conditions on t and k for the existence of a k-extended Skolem-type 5-tuple difference set ...

Each of the elements of this list is itself a partition, and the numbers in each partition are referred to as parts . As one may clearly deduce, the larger the number, the more partitions it has. Also of note is the fact that is the same as , that is, order is not accounted for. Typically, the parts of a partition are written in nonincreasing order. It is also commonly accepted that the functio...