A summary of noncyclic difference sets, k < 20

A Summary of Menon Difference Sets

A Brief Survey of Difference Sets, Partial Difference Sets, and Relative Difference Sets

Difference sets, partial difference sets, and relative difference sets are algebraic structures with combinatorial applications. The purpose of this paper is to give the reader definitions and basic examples of these sets, as well describe their connections to some other well-known combinatorial objects. We will conclude with some examples that illustrate how character theory can be used to pro...

Nonabelian Groups with (96, 20, 4) Difference Sets

We resolve the existence problem of (96, 20, 4) difference sets in 211 of 231 groups of order 96. If G is a group of order 96 with normal subgroups of orders 3 and 4 then by first computing 32and 24-factor images of a hypothetical (96, 20, 4) difference set in G we are able to either construct a difference set or show a difference set does not exist. Of the 231 groups of order 96, 90 groups adm...

$k$-Total difference cordial graphs

Let $G$ be a graph. Let $f:V(G)to{0,1,2, ldots, k-1}$ be a map where $k in mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $left|f(u)-f(v)right|$. $f$ is called a $k$-total difference cordial labeling of $G$ if $left|t_{df}(i)-t_{df}(j)right|leq 1$, $i,j in {0,1,2, ldots, k-1}$ where $t_{df}(x)$ denotes the total number of vertices and the edges labeled with $x$.A graph with admits a...

Number of Minimal Path Sets in a Consecutive-k-out-of-n: F System

In this paper the combinatorial problem of determining the number of minimal path sets of a consecutive-k-out-of-n: F system is considered. For the cases where k = 2, 3 the explicit formulae are given and for k &ge; 4 a recursive relation is obtained. Direct computation for determining the number of minimal path sets of a consecutive-k-out-of-n: F system for k &ge; 4 remains a difficult task. ...