2017
6
3
3
0
Common extremal graphs for three inequalities involving domination parameters
2
2
Let $delta (G)$, $Delta (G)$ and $gamma(G)$ be the minimum degree, maximum degree and domination number of a graph $G=(V(G), E(G))$, respectively. A partition of $V(G)$, all of whose classes are dominating sets in $G$, is called a domatic partition of $G$. The maximum number of classes of a domatic partition of $G$ is called the domatic number of $G$, denoted $d(G)$. It is well known that $d(G) leq delta(G) + 1$, $d(G)gamma(G) leq V(G)$ cite{ch}, and $V(G) leq (Delta(G)+1)gamma(G)$ cite{berge}. In this paper, we investigate the graphs $G$ for which all the above inequalities become simultaneously equalities.
1

1
9


Vladimir
Samodivkin
University of Architecture, Civil Engineering and Geodesy (UACEG)
University of Architecture, Civil Engineering
Bulgaria
vl.samodivkin@gmail.com
domination/domatic/idomatic number
efficient dominating set
On the hilbert series of binomial edge ideals of generalized trees
2
2
In this paper we introduce the concept of generalized trees and compute the Hilbert series of their binomial edge ideals.
1

11
18


Farhad
Rahmati
Amirkabir University of Technology
Amirkabir University of Technology
Iran
frahmati@aut.ac.ir


Mahdis
Saeedi
Amirkabir University of Technology
Amirkabir University of Technology
Iran
mahdis_saeedi@yahoo.com
binomial edge ideal
hilbert series
short exact sequence
Binary sequence/array pairs via diference set pairs: A recursive approach
2
2
Binary array pairs with optimal/ideal correlation values and their algebraic counterparts textquotedblleft difference set pairstextquotedblright;(DSPs) in abelian groups are studied. In addition to generalizing known 1dimensional (sequences) examples, we provide four new recursive constructions, unifying previously obtained ones. Any further advancements in the construction of binary sequences/arrays with optimal/ideal correlation values (equivalently cyclic/abelian difference sets) would give rise to richer classes of DSPs (and hence binary perfect array pairs). Discrete signals arising from DSPs find applications in cryptography, CDMA systems, radar and wireless communications.
1

19
36


K. T.
Arasu
Wright State University
Wright State University
United States of America
k.arasu@wright.edu


Anika
Goyal
Dept. of Computer Engg., YMCA University of Science And Technology, Faridabad, HR 121006, India
Dept. of Computer Engg., YMCA University
India
anikagoyal13@gmail.com


Abhishek
Puri
Dept. of Computer Engg., YMCA University of Science And Technology, Faridabad, HR 121006, India
Dept. of Computer Engg., YMCA University
India
puri.abhishek14@gmail.com
autocorrelation
binary sequence
perfect sequence pair
difference set pair
A class of Ramseyextremal hypergraphs
2
2
In 1991, McKay and Radziszowski proved that, however each $3$subset of a $13$set is assigned one of two colours, there is some $4$subset whose four $3$subsets have the same colour. More than 25 years later, this remains the only nontrivial classical Ramsey number known for hypergraphs. In this article, we find all the extremal colourings of the $3$subsets of a 12set and list some of their properties. We also provide an answer to a question of Dudek, La Fleur, Mubayi and R"odl about the sizeRamsey numbers of hypergraphs.
1

37
43


Brendan D.
McKay
Australian National University
Australian National University
Austria
brendan.mckay@anu.edu.au
hypergraph
Ramsey number
sizeRamsey number
Distance in cayley graphs on permutation groups generated by $k$ $m$Cycles
2
2
In this paper, we extend upon the results of B. Suceav{u{a}} and R. Stong [Amer. Math. Monthly, 110 (2003) 162162], which they computed the minimum number of 3cycles needed to generate an even permutation. Let $Omega^n_{k,m}$ be the set of all permutations of the form $c_1 c_2 cdots c_k$ where $c_i$'s are arbitrary $m$cycles in $S_n$. Suppose that $Gamma^n_{k,m}$ be the Cayley graph on subgroup of $S_n$ generated by all permutations in $Omega^n_{k,m}$. We find a shortest path joining identity and any vertex of $Gamma^n_{k,m}$, for arbitrary natural number $k$, and $m=2 , , 3,, 4$. Also, we calculate the diameter of these Cayley graphs. As an application, we present an algorithm for finding a short expression of a permutation as products of given permutations.
1

45
59


Zohreh
Mostaghim
Iran University of Science and Technology
Iran University of Science and Technology
Iran
mostaghim@iust.ac.ir


Mohammad Hossein
Ghaffari
Iran University of Science and Technology
Iran University of Science and Technology
Iran
mhghaffari@iust.ac.ir
Permutation group
Cayley graph
Quadruple cycles
Diameter
Expressions of permutations