eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-06-01
2
2
1
7
10.22108/toc.2013.2840
2840
On the complexity of the colorful directed paths in vertex coloring of digraphs
S. Saqaeeyan
1
Esmaeil Mollaahmadi
mollaahmadi@gmail.com
2
Ali Dehghan
ali_dehghan16@aut.ac.ir
3
Abadan Branch, Islamic Azad University
Sharif University of Technology .
Amirkabir University of Technology, Tehran, Iran
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.
http://toc.ui.ac.ir/article_2840_6a5c24f33fd5a66915e473e2c44ca4aa.pdf
Colorful Directed Paths
Computational Complexity
Vertex Coloring
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-06-01
2
2
9
17
10.22108/toc.2013.2848
2848
Convolutional cylinder-type block-circulant cycle codes
Mohammad Gholami
gholamimoh@gmail.com
1
Mehdi Samadieh
m.samadieh@mathhouse.org
2
Shahrekord University
Isfahan Mathematics House
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.
http://toc.ui.ac.ir/article_2848_9c85537997b5b347da497a3d38139266.pdf
LDPC codes
convolutional codes
Girth
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-06-01
2
2
19
26
10.22108/toc.2013.2869
2869
On schemes originated from Ferrero pairs
Hossein Moshtagh
moshtagh@dena.kntu.ac.ir
1
Amir Rahnamai Barghi
rahnama@kntu.ac.ir
2
Department of Mathematics, K. N. Toosi University of Technology,
K. N. Toosi university of Technology University, Tehran-Iran.
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.
http://toc.ui.ac.ir/article_2869_9eaaa1dafa631de15cb2c9f513a98e5c.pdf
Frobenius group
Oribtal
Scheme
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-06-01
2
2
27
33
10.22108/toc.2013.2872
2872
On the number of cliques and cycles in graphs
Masoud Ariannejad
m.ariannejad@gmail.com
1
Mojgan Emami
mojgan.emami@yahoo.com
2
University of zanjan
Department of Mathematics, University of Zanjan
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 $G$.
http://toc.ui.ac.ir/article_2872_183b76bba4970596525b994ca1ef4997.pdf
graph
cycle
Clique
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-06-01
2
2
35
40
10.22108/toc.2013.2881
2881
Probabilistic analysis of the first Zagreb index
Ramin Kazemi
kazemi@ikiu.ac.ir
1
Department of statistics, Imam Khomeini International University, Qazvin
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.
http://toc.ui.ac.ir/article_2881_e4d82056fd1c36fd883f73551fe4a60f.pdf
Bucket recursive trees with variable capacities
of buckets
Zagreb index
martingale
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-06-01
2
2
41
46
10.22108/toc.2013.2890
2890
On the spectra of reduced distance matrix of dendrimers
Abbas Heydari
a-heidari@iau-arak.ac.ir
1
staff
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.
http://toc.ui.ac.ir/article_2890_73b2bef50330eda9f10bd13a01debf78.pdf
Reduced distance matrix
spectrum
Regular Dendrimers
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-06-01
2
2
47
72
10.22108/toc.2013.2943
2943
Modular chromatic number of $C_m square P_n$
N. Paramaguru
1
R. Sampathkumar
2
Annamalai University
Annamalai University
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.
http://toc.ui.ac.ir/article_2943_5fa15d9e433e3cf4e5d1849c0214c4df.pdf
modular coloring
modular chromatic number
Cartesian product