The common minimal common neighborhood dominating signed graphs
P. Siva
Reddy
Dept. of Mathematics, Acharya Institute of Technology, Bangalore-560 090, India.
author
K. R.
Rajanna
Professor and Head
Dept. of Mathematics
Acharya Institute of Technology
Bangalore-560 090
India
author
Kavita
Permi
Assistant Professor
Dept.of Mathematics
Acharya Institute of Technology
Bangalore-560 090
India.
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
1
no.
2013
1
8
http://toc.ui.ac.ir/article_2640_a723658d1a823e061445180f458832f4.pdf
dx.doi.org/10.22108/toc.2013.2640
Bounding the domination number of a tree in terms of its annihilation number
Nasrin
Dehgardai
Azarbaijan Shahid Madani University
author
Sepideh
Norouzian
Azarbaijan Shahid Madani University
author
Seyed Mahmoud
Sheikholeslami
Azarbaijan University of Tarbiat Moallem
author
text
article
2013
eng
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 $n\ge 2$, $\gamma(T)\le \frac{3a(T)+2}{4}$, and we characterize the trees achieving this bound.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
1
no.
2013
9
16
http://toc.ui.ac.ir/article_2652_424dc767de5dc6d68475c6d0b1d46b2e.pdf
dx.doi.org/10.22108/toc.2013.2652
Gray isometries for finite $p$-groups
Reza
Sobhani
author
text
article
2013
eng
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 $\psi:H\longrightarrow {\rm Aut}(K)$ 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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
1
no.
2013
17
26
http://toc.ui.ac.ir/article_2762_9284f3f283a59b2d3778fed1f1d9bbfd.pdf
dx.doi.org/10.22108/toc.2013.2762
New skew Laplacian energy of simple digraphs
Qingqiong
Cai
Center for Combinatorics, nankai University, Tianjin, China
author
Xueliang
Li
Center for Combinatorics, Nankai University, Tianjin 300071, China
author
Jiangli
Song
Center for Combinatorics, Nankai University, Tianjin, China
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
1
no.
2013
27
37
http://toc.ui.ac.ir/article_2833_dc29c895a9ecdf11e850c68593ab72de.pdf
dx.doi.org/10.22108/toc.2013.2833
A comprehensive survey: Applications of multi-objective particle swarm optimization (MOPSO) algorithm
Soniya
Lalwani
Statistician, R & D, Advanced Bioinformatics Centre, Birla Institute of Scientific Research, Jaipur
PhD student, Department of Mathematics, Malaviya National Institute of Technology, Jaipur
author
Sorabh
Singhal
Project student, R & D, Advanced Bioinformatics Centre, Birla Institute of Scientific Research, Jaipur
author
Rajesh
Kumar
Associate Professor, Department of Electrical Engineering, Malaviya National Institute of Technology, Jaipur
author
Nilama
Gupta
Associate Professor, Department of Mathematics, Malaviya National Institute of Technology, Jaipur
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
1
no.
2013
39
101
http://toc.ui.ac.ir/article_2834_41014f74d9dba356c8e6249253ea38f9.pdf
dx.doi.org/10.22108/toc.2013.2834
Eccentric connectivity index and eccentric distance sum of some graph operations
Buzohragul
Eskender
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P.R. China
author
Elkin
Vumar
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
author
text
article
2013
eng
Let $G=(V,E)$ be a connected graph. The eccentric connectivity index of $G$, $\xi^{c}(G)$, is defined as
$\xi^{c}(G)=\sum_{v\in V(G)}deg(v)ec(v)$, 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 $\xi^{d}(G)=\sum_{v\in V(G)}ec(v)D(v)$, where $D(v)=\sum_{u\in V(G)}d(u,v)$. 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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
1
no.
2013
103
111
http://toc.ui.ac.ir/article_2839_841442d18d11e9fd56842e8df7e42010.pdf
dx.doi.org/10.22108/toc.2013.2839