eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-03-01
2
1
1
8
10.22108/toc.2013.2640
2640
The common minimal common neighborhood dominating signed graphs
P. Siva Reddy
reddy_math@yahoo.com
1
K. R. Rajanna
rajanna@acharya.ac.in
2
Kavita Permi
kavithapermi@acharya.ac.in
3
Dept. of Mathematics, Acharya Institute of Technology, Bangalore-560 090, India.
Professor and Head Dept. of Mathematics Acharya Institute of Technology Bangalore-560 090 India
Assistant Professor Dept.of Mathematics Acharya Institute of Technology Bangalore-560 090 India.
In this paper, we define the common minimal common neighborhood dominating signed graph (or common minimal $CN$-dominating signed graph) of a given signed graph and offer a structural characterization of common minimal $CN$-dominating signed graphs. In the sequel, we also obtained switching equivalence
characterization: $overline{Sigma} sim CMCN(Sigma)$, where $overline{Sigma}$ and $CMCN(Sigma)$ are complementary signed graph and common minimal $CN$-signed graph of $Sigma$ respectively.
http://toc.ui.ac.ir/article_2640_a723658d1a823e061445180f458832f4.pdf
Signed graphs
Balance
Switching
Common minimal $CN$-dominating signed graph
Negation
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-03-01
2
1
9
16
10.22108/toc.2013.2652
2652
Bounding the domination number of a tree in terms of its annihilation number
Nasrin Dehgardai
ndehgardi@gmail.com
1
Sepideh Norouzian
s_maleki494@yahoo.com
2
Seyed Mahmoud Sheikholeslami
s.m.sheikholeslami@azaruniv.edu
3
Azarbaijan Shahid Madani University
Azarbaijan Shahid Madani University
Azarbaijan University of Tarbiat Moallem
A set $S$ of vertices in a graph $G$ is a dominating set if every vertex of $V-S$ is adjacent to some vertex in $S$. The domination number $gamma(G)$ is the minimum cardinality of a dominating set in $G$. The annihilation number $a(G)$ is the largest integer $k$ such that the sum of the first $k$ terms of the non-decreasing degree sequence of $G$ is at most the number of edges in $G$. In this paper, we show that for any tree $T$ of order $nge 2$, $gamma(T)le frac{3a(T)+2}{4}$, and we characterize the trees achieving this bound.
http://toc.ui.ac.ir/article_2652_424dc767de5dc6d68475c6d0b1d46b2e.pdf
annihilation number
dominating set
Domination Number
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-03-01
2
1
17
26
10.22108/toc.2013.2762
2762
Gray isometries for finite $p$-groups
Reza Sobhani
r.sobhani@sci.ui.ac.ir
1
We construct two classes of Gray maps, called type-I Gray map and type-II Gray map, for a finite $p$-group $G$. Type-I Gray maps are constructed based on the existence of a Gray map for a maximal subgroup $H$ of $G$. When $G$ is a semidirect product of two finite $p$-groups $H$ and $K$, both $H$ and $K$ admit Gray maps and the corresponding homomorphism $psi:Hlongrightarrow {rm Aut}(K)$ is compatible with the Gray map of $K$ in a sense which we will explain, we construct type-II Gray maps for $G$. Finally, we consider group codes over the dihedral group $D_8$ of order 8 given by the set of their generators, and derive a representation and an encoding procedure for such codes.
http://toc.ui.ac.ir/article_2762_9284f3f283a59b2d3778fed1f1d9bbfd.pdf
Finite group
Code
Gray map
Isometry
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-03-01
2
1
27
37
10.22108/toc.2013.2833
2833
New skew Laplacian energy of simple digraphs
Qingqiong Cai
cqqnjnu620@163.com
1
Xueliang Li
lxl@nankai.edu.cn
2
Jiangli Song
songjiangli@mail.nankai.edu.cn
3
Center for Combinatorics, nankai University, Tianjin, China
Center for Combinatorics, Nankai University, Tianjin 300071, China
Center for Combinatorics, Nankai University, Tianjin, China
For a simple digraph $G$ of order $n$ with vertex set ${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote the out-degree and in-degree of a vertex $v_i$ in $G$, respectively. Let $D^+(G)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and $D^-(G)=diag(d_1^-,d_2^-,ldots,d_n^-)$. In this paper we introduce $widetilde{SL}(G)=widetilde{D}(G)-S(G)$ to be a new kind of skew Laplacian matrix of $G$, where $widetilde{D}(G)=D^+(G)-D^-(G)$ and $S(G)$ is the skew-adjacency matrix of $G$, and from which we define the skew Laplacian energy $SLE(G)$ of $G$ as the sum of the norms of all the eigenvalues of $widetilde{SL}(G)$. Some lower and upper bounds of the new skew Laplacian energy are derived and the digraphs attaining these bounds are also determined.
http://toc.ui.ac.ir/article_2833_dc29c895a9ecdf11e850c68593ab72de.pdf
energy
Laplacian energy
skew energy
skew Laplacian energy
eigenvalues
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-03-01
2
1
39
101
10.22108/toc.2013.2834
2834
A comprehensive survey: Applications of multi-objective particle swarm optimization (MOPSO) algorithm
Soniya Lalwani
slalwani.math@gmail.com
1
Sorabh Singhal
saurabhez@gmail.com
2
Rajesh Kumar
rkumar.ee@gmail.com
3
Nilama Gupta
guptanilama@gmail.com
4
Statistician, R & D, Advanced Bioinformatics Centre, Birla Institute of Scientific Research, Jaipur PhD student, Department of Mathematics, Malaviya National Institute of Technology, Jaipur
Project student, R & D, Advanced Bioinformatics Centre, Birla Institute of Scientific Research, Jaipur
Associate Professor, Department of Electrical Engineering, Malaviya National Institute of Technology, Jaipur
Associate Professor, Department of Mathematics, Malaviya National Institute of Technology, Jaipur
Numerous problems encountered in real life cannot be actually formulated as a single objective problem; hence the requirement of Multi-Objective Optimization (MOO) had arisen several years ago. Due to the complexities in such type of problems powerful heuristic techniques were needed, which has been strongly satisfied by Swarm Intelligence (SI) techniques. Particle Swarm Optimization (PSO) has been established in 1995 and became a very mature and most popular domain in SI. Multi-Objective PSO (MOPSO) established in 1999, has become an emerging field for solving MOOs with a large number of extensive literature, software, variants, codes and applications. This paper reviews all the applications of MOPSO in miscellaneous areas followed by the study on MOPSO variants in our next publication. An introduction to the key concepts in MOO is followed by the main body of review containing survey of existing work, organized by application area along with their multiple objectives, variants and further categorized variants.
http://toc.ui.ac.ir/article_2834_41014f74d9dba356c8e6249253ea38f9.pdf
Multi-Objective Particle Swarm Optimization
Conflicting objectives
Particle swarm optimization
Pareto optimal set
Non-dominated solutions
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-03-01
2
1
103
111
10.22108/toc.2013.2839
2839
Eccentric connectivity index and eccentric distance sum of some graph operations
Buzohragul Eskender
buzoragul2005@163.com
1
Elkin Vumar
vumar@xju.edu.cn
2
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P.R. China
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Let $G=(V,E)$ be a connected graph. The eccentric connectivity index of $G$, $xi^{c}(G)$, is defined as
$xi^{c}(G)=sum_{vin V(G)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. The eccentric distance sum of $G$ is defined as $xi^{d}(G)=sum_{vin V(G)}ec(v)D(v)$, where $D(v)=sum_{uin V(G)}d(u,v)$. In this paper, we calculate the eccentric connectivity index and eccentric distance sum of generalized hierarchical product of graphs. Moreover, we present the exact formulae for the eccentric connectivity index of $F$-sum graphs in terms of some invariants of the factors.
http://toc.ui.ac.ir/article_2839_841442d18d11e9fd56842e8df7e42010.pdf
Eccentric connectivity index
eccentric distance sum
generalized hierarchical product
$F$-sum graphs