University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
3
2017
09
01
Common extremal graphs for three inequalities involving domination parameters
1
9
EN
Vladimir
Samodivkin
University of Architecture, Civil Engineering and Geodesy (UACEG)
vl.samodivkin@gmail.com
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.
domination/domatic/idomatic number,efficient dominating set
http://toc.ui.ac.ir/article_21464.html
http://toc.ui.ac.ir/article_21464_e634e304e912f76a101c385fa80076eb.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
3
2017
09
01
On the hilbert series of binomial edge ideals of generalized trees
11
18
EN
Farhad
Rahmati
Amirkabir University of Technology
frahmati@aut.ac.ir
Mahdis
Saeedi
Amirkabir University of Technology
mahdis_saeedi@yahoo.com
In this paper we introduce the concept of generalized trees and compute the Hilbert series of their binomial edge ideals.
binomial edge ideal,hilbert series,short exact sequence
http://toc.ui.ac.ir/article_21463.html
http://toc.ui.ac.ir/article_21463_658ac2a187cd8b5573536a652113719e.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
3
2017
09
01
Binary sequence/array pairs via diference set pairs: A recursive approach
19
36
EN
K. T.
Arasu
Wright State University
k.arasu@wright.edu
Anika
Goyal
Dept. of Computer Engg., YMCA University of Science And Technology, Faridabad, HR 121006, India
anikagoyal13@gmail.com
Abhishek
Puri
Dept. of Computer Engg., YMCA University of Science And Technology, Faridabad, HR 121006, India
puri.abhishek14@gmail.com
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 1-dimensional (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.
autocorrelation,binary sequence,perfect sequence pair,difference set pair
http://toc.ui.ac.ir/article_21466.html
http://toc.ui.ac.ir/article_21466_7872b534dc27cd9c3fa2ab7a0cb15ba8.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
3
2017
09
01
A class of Ramsey-extremal hypergraphs
37
43
EN
Brendan D.
McKay
Australian National University
brendan.mckay@anu.edu.au
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 non-trivial classical Ramsey number known for hypergraphs. In this article, we find all the extremal colourings of the $3$-subsets of a 12-set and list some of their properties. We also provide an answer to a question of Dudek, La Fleur, Mubayi and R"odl about the size-Ramsey numbers of hypergraphs.
hypergraph,Ramsey number,size-Ramsey number
http://toc.ui.ac.ir/article_21468.html
http://toc.ui.ac.ir/article_21468_114fdfc65b03414f07a821ae0e7d6b38.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
6
3
2017
09
01
Distance in cayley graphs on permutation groups generated by $k$ $m$-Cycles
45
59
EN
Zohreh
Mostaghim
Iran University of Science and Technology
mostaghim@iust.ac.ir
Mohammad Hossein
Ghaffari
Iran University of Science and Technology
mhghaffari@iust.ac.ir
In this paper, we extend upon the results of B. Suceav{u{a}} and R. Stong [Amer. Math. Monthly, 110 (2003) 162--162], which they computed the minimum number of 3-cycles 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.
Permutation group,Cayley graph,Quadruple cycles,Diameter,Expressions of permutations
http://toc.ui.ac.ir/article_21473.html
http://toc.ui.ac.ir/article_21473_2e07c04c5fad360f2c8b9fc03265c648.pdf