University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2
2
2013
06
01
On the complexity of the colorful directed paths in vertex coloring of digraphs
1
7
EN
S.
Saqaeeyan
Abadan Branch, Islamic Azad University
Esmaeil
Mollaahmadi
Sharif University of Technology .
mollaahmadi@gmail.com
Ali
Dehghan
Amirkabir University of Technology, Tehran, Iran
ali_dehghan16@aut.ac.ir
10.22108/toc.2013.2840
The colorful paths and rainbow paths have been considered by several authors. A colorful directed path in a digraph $G$ is a directed path with $chi(G)$ vertices whose colors are different. A $v$-colorful directed path is such a directed path, starting from $v$. We prove that for a given $3$-regular triangle-free digraph $G$ determining whether there is a proper $chi(G)$-coloring of $G$ such that for every $v in V (G)$, there exists a $v$-colorful directed path is $ mathbf{NP} $-complete.
Colorful Directed Paths,Computational Complexity,Vertex Coloring
http://toc.ui.ac.ir/article_2840.html
http://toc.ui.ac.ir/article_2840_6a5c24f33fd5a66915e473e2c44ca4aa.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2
2
2013
06
01
Convolutional cylinder-type block-circulant cycle codes
9
17
EN
Mohammad
Gholami
Shahrekord University
gholamimoh@gmail.com
Mehdi
Samadieh
Isfahan Mathematics House
m.samadieh@mathhouse.org
10.22108/toc.2013.2848
In this paper, we consider a class of column-weight two quasi-cyclic low-density parity check codes in which the girth can be large enough, as an arbitrary multiple of 8. Then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. Finally, we show that the free distance of the convolutional codes is equal to the minimum distance of
their block counterparts.
LDPC codes,convolutional codes,Girth
http://toc.ui.ac.ir/article_2848.html
http://toc.ui.ac.ir/article_2848_9c85537997b5b347da497a3d38139266.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2
2
2013
06
01
On schemes originated from Ferrero pairs
19
26
EN
Hossein
Moshtagh
Department of
Mathematics, K. N. Toosi University of Technology,
moshtagh@dena.kntu.ac.ir
Amir
Rahnamai Barghi
K. N. Toosi university of Technology University, Tehran-Iran.
rahnama@kntu.ac.ir
10.22108/toc.2013.2869
The Frobenius complement of a given Frobenius group acts on its kernel. The scheme which is arisen from the orbitals of this action is called Ferrero pair scheme. In this paper, we show that the fibers of a Ferrero pair scheme consist of exactly one singleton fiber and every two fibers with more than one point have the same cardinality. Moreover, it is shown that the restriction of a Ferrero pair scheme on each fiber is isomorphic to a regular scheme. Finally, we prove that for any prime $p$, there exists a Ferrero pair $p$-scheme, and if $p> 2$, then the Ferrero pair $p$-schemes of the same rank are all isomorphic.
Frobenius group,Oribtal,Scheme
http://toc.ui.ac.ir/article_2869.html
http://toc.ui.ac.ir/article_2869_9eaaa1dafa631de15cb2c9f513a98e5c.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2
2
2013
06
01
On the number of cliques and cycles in graphs
27
33
EN
Masoud
Ariannejad
University of zanjan
m.ariannejad@gmail.com
Mojgan
Emami
Department of Mathematics, University of Zanjan
mojgan.emami@yahoo.com
10.22108/toc.2013.2872
We give a new recursive method to compute the number of cliques and cycles of a graph. This method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the adjacency matrix of the graph. In particular, let $G$ be a graph and let $overline {G}$ be its complement, then given the chromatic polynomial of $overline {G}$, we give a recursive method to compute the number of cliques of $G$. Also given the adjacency matrix $A$ of $G$ we give a recursive method to compute the number of cycles by computing the sum of permanent function of the principal minors of $A$. In both cases we confront to a new computable parameter which is defined as the number of disjoint cliques in $G$.
graph,cycle,Clique
http://toc.ui.ac.ir/article_2872.html
http://toc.ui.ac.ir/article_2872_183b76bba4970596525b994ca1ef4997.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2
2
2013
06
01
Probabilistic analysis of the first Zagreb index
35
40
EN
Ramin
Kazemi
Department of statistics, Imam Khomeini International University, Qazvin
kazemi@ikiu.ac.ir
10.22108/toc.2013.2881
In this paper we study the first Zagreb index in bucket recursive trees containing buckets with variable capacities. This model was introduced by Kazemi in 2012. We obtain the mean and variance of the first Zagreb index and introduce a martingale based on this quantity.
Bucket recursive trees with variable capacities
of buckets,Zagreb index,martingale
http://toc.ui.ac.ir/article_2881.html
http://toc.ui.ac.ir/article_2881_e4d82056fd1c36fd883f73551fe4a60f.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2
2
2013
06
01
On the spectra of reduced distance matrix of dendrimers
41
46
EN
Abbas
Heydari
staff
a-heidari@iau-arak.ac.ir
10.22108/toc.2013.2890
Let $G$ be a simple connected graph and ${v_1,v_2,ldots, v_k}$ be the set of pendent (vertices of degree one) vertices of $G$. The reduced distance matrix of $G$ is a square matrix whose $(i,j)$-entry is the topological distance between $v_i$ and $v_j$ of $G$. In this paper, we obtain the spectrum of the reduced distance matrix of regular dendrimers.
Reduced distance matrix,spectrum,Regular Dendrimers
http://toc.ui.ac.ir/article_2890.html
http://toc.ui.ac.ir/article_2890_73b2bef50330eda9f10bd13a01debf78.pdf
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2
2
2013
06
01
Modular chromatic number of $C_m square P_n$
47
72
EN
N.
Paramaguru
Annamalai University
R.
Sampathkumar
Annamalai University
10.22108/toc.2013.2943
A modular $k!$-coloring, $kge 2,$ of a graph $G$ is a coloring of the vertices of $G$ with the elements in $mathbb{Z}_k$ having the property that for every two adjacent vertices of $G,$ the sums of the colors of their neighbors are different in $mathbb{Z}_k.$ The minimum $k$ for which $G$ has a modular $k!$-coloring is the modular chromatic number of $G.$ Except for some special cases, modular chromatic number of $C_msquare P_n$ is determined.
modular coloring,modular chromatic number,Cartesian product
http://toc.ui.ac.ir/article_2943.html
http://toc.ui.ac.ir/article_2943_5fa15d9e433e3cf4e5d1849c0214c4df.pdf