On the girth of Tanner (3,7) quasi-cyclic LDPC codes
Mohammad
Gholami
Shahrekord University
author
Fahime
Mostafaiee
Malek Ashtar University
author
text
article
2012
eng
S. Kim et al. have been analyzed the girth of some algebraically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes, i.e. Tanner $(3,5)$ of length $5p$, where $p$ is a prime of the form $15m+1$. In this paper, by extension this method to Tanner $(3,7)$ codes of length $7p$, where $p$ is a prime of the form $21m+ 1$, the girth values of Tanner $(3,7)$ codes will be derived. As an advantage, the rate of Tanner $(3,7)$ codes is about $0.17$ more than the rate of Tanner $(3,5)$ codes.
Transactions on Combinatorics
University of Isfahan
2251-8657
1
v.
2
no.
2012
1
16
http://toc.ui.ac.ir/article_762_85296de6ff7eb52d8ed768223d7e820d.pdf
dx.doi.org/10.22108/toc.2012.762
Connected cototal domination number of a graph
B.
Basavanagoud
Karnatak University
author
Sunilkumar
Hosamani
Karnatak University, Dharwad
author
text
article
2012
eng
A dominating set $D \subseteq V$ of a graph $G = (V,E)$ is said to be a connected cototal dominating set if $\langle D \rangle$ is connected and $\langle V-D \rangle \neq \varnothing $, contains no isolated vertices. A connected cototal dominating set is said to be minimal if no proper subset of $D$ is connected cototal dominating set. The connected cototal domination number $\gamma_{ccl}(G)$ of $G$ is the minimum cardinality of a minimal connected cototal dominating set of $G$. In this paper, we begin an investigation of connected cototal domination number and obtain some interesting results.
Transactions on Combinatorics
University of Isfahan
2251-8657
1
v.
2
no.
2012
17
26
http://toc.ui.ac.ir/article_820_bd185d6e0dce9d0bea5fb29b49ff1348.pdf
dx.doi.org/10.22108/toc.2012.820
Degree resistance distance of unicyclic graphs
Ivan
Gutman
University of Kragujevac
Kragujevac, Serbia
author
Linhua
Feng
Department of Mathematics, Central South University
author
Guihai
Yu
Department of Mathematics, Central South University
author
text
article
2012
eng
Let $G$ be a connected graph with vertex set $V(G)$. The degree resistance distance of $G$ is defined as $D_R(G) = \sum_{\{u, v\} \subseteq V(G)} [d(u)+d(v)] R(u,v)$, where $d(u)$ is the degree of vertex $u$, and $R(u,v)$ denotes the resistance distance between $u$ and $v$. In this paper, we characterize $n$-vertex unicyclic graphs having minimum and second minimum degree resistance distance.
Transactions on Combinatorics
University of Isfahan
2251-8657
1
v.
2
no.
2012
27
40
http://toc.ui.ac.ir/article_1080_cb45bc3cac05fe499d71eb2ac6e5ec20.pdf
dx.doi.org/10.22108/toc.2012.1080
Some results on characterization of finite group by non commuting graph
Mohammad Reza
Darafsheh
University of Tehran
author
Pedram
Yousefzadeh
K. N. Toosi University of Technology
author
text
article
2012
eng
The non commuting graph $\nabla(G)$ of a non-abelian finite group $G$ is defined as follows: its vertex set is $G- Z (G)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. In this paper we prove some new results about this graph. In particular we will give a new proof of Theorem 3.24 of [A. Abdollahi, S. Akbari, H. R, Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006) 468-492.]. We also prove that if $G_1, G_2, \ldots, G_n$ are finite groups such that $Z(G_i)=1$ for $i=1, 2,\ldots, n$ and they are characterizable by non commuting graph, then $G_1 \times G_2 \times \cdots \times G_n$ is characterizable by non-commuting graph.
Transactions on Combinatorics
University of Isfahan
2251-8657
1
v.
2
no.
2012
41
48
http://toc.ui.ac.ir/article_1180_0ca13861eb689e095c1f50d1542a1aa7.pdf
dx.doi.org/10.22108/toc.2012.1180
On the values of independence and domination polynomials at specific points
Saeid
Alikhani
Yazd University
author
Mohammad
Reyhani
Islamic Azad University
author
text
article
2012
eng
Let $G$ be a simple graph of order $n$. We consider the independence polynomial and the domination polynomial of a graph $G$. The value of a graph polynomial at a specific point can give sometimes a very surprising information about the structure of the graph. In this paper we investigate independence and domination polynomial at $-1$ and $1$.
Transactions on Combinatorics
University of Isfahan
2251-8657
1
v.
2
no.
2012
49
57
http://toc.ui.ac.ir/article_1484_e42846496835542c7075da7bc53a2edc.pdf
dx.doi.org/10.22108/toc.2012.1484
The order difference interval graph of a group
P.
Balakrishnan
Department of Mathematics,
Manonmaniam Sundaranar University, tirunelveli
author
R.
Kala
Department of Mathematics
Manonmaniam Sundaranar University
Tirunelveli 627 012, Tamil Nadu, India.
author
text
article
2012
eng
In this paper we introduce the concept of order difference interval graph $\Gamma_{ODI}(G)$ of a group $G$. It is a graph $\Gamma_{ODI}(G)$ with $V(\Gamma_{ODI}(G)) = G$ and two vertices $a$ and $b$ are adjacent in $\Gamma_{ODI}(G)$ if and only if $o(b)-o(a) \in [o(a), o(b)]$. Without loss of generality, we assume that $o(a) \leq o(b)$. In this paper we obtain several properties of $\Gamma_{ODI}(G)$, upper bounds on the number of edges of $\Gamma_{ODI}(G)$ and determine those groups whose order difference interval graph is isomorphic to a complete multipartite graph.
Transactions on Combinatorics
University of Isfahan
2251-8657
1
v.
2
no.
2012
59
65
http://toc.ui.ac.ir/article_1588_9fb8176991b10ac13f1c1c7d632dd893.pdf
dx.doi.org/10.22108/toc.2012.1588