On the complexity of the colorful directed paths in vertex coloring of digraphs
S.
Saqaeeyan
Abadan Branch, Islamic Azad University
author
Esmaeil
Mollaahmadi
Sharif University of Technology .
author
Ali
Dehghan
Amirkabir University of Technology, Tehran, Iran
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
2
no.
2013
1
7
http://toc.ui.ac.ir/article_2840_6a5c24f33fd5a66915e473e2c44ca4aa.pdf
dx.doi.org/10.22108/toc.2013.2840
Convolutional cylinder-type block-circulant cycle codes
Mohammad
Gholami
Shahrekord University
author
Mehdi
Samadieh
Isfahan Mathematics House
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
2
no.
2013
9
17
http://toc.ui.ac.ir/article_2848_9c85537997b5b347da497a3d38139266.pdf
dx.doi.org/10.22108/toc.2013.2848
On schemes originated from Ferrero pairs
Hossein
Moshtagh
Department of
Mathematics, K. N. Toosi University of Technology,
author
Amir
Rahnamai Barghi
K. N. Toosi university of Technology University, Tehran-Iran.
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
2
no.
2013
19
26
http://toc.ui.ac.ir/article_2869_9eaaa1dafa631de15cb2c9f513a98e5c.pdf
dx.doi.org/10.22108/toc.2013.2869
On the number of cliques and cycles in graphs
Masoud
Ariannejad
University of zanjan
author
Mojgan
Emami
Department of Mathematics, University of Zanjan
author
text
article
2013
eng
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 $G$.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
2
no.
2013
27
33
http://toc.ui.ac.ir/article_2872_183b76bba4970596525b994ca1ef4997.pdf
dx.doi.org/10.22108/toc.2013.2872
Probabilistic analysis of the first Zagreb index
Ramin
Kazemi
Department of statistics, Imam Khomeini International University, Qazvin
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
2
no.
2013
35
40
http://toc.ui.ac.ir/article_2881_e4d82056fd1c36fd883f73551fe4a60f.pdf
dx.doi.org/10.22108/toc.2013.2881
On the spectra of reduced distance matrix of dendrimers
Abbas
Heydari
staff
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
2
no.
2013
41
46
http://toc.ui.ac.ir/article_2890_73b2bef50330eda9f10bd13a01debf78.pdf
dx.doi.org/10.22108/toc.2013.2890
Modular chromatic number of $C_m \square P_n$
N.
Paramaguru
Annamalai University
author
R.
Sampathkumar
Annamalai University
author
text
article
2013
eng
A modular $k\!$-coloring, $k\ge 2,$ 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 $C_m\square P_n$ is determined.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
2
no.
2013
47
72
http://toc.ui.ac.ir/article_2943_5fa15d9e433e3cf4e5d1849c0214c4df.pdf
dx.doi.org/10.22108/toc.2013.2943