eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-09-01
2
3
1
11
3002
On the nomura algebras of formally self-dual association schemes of class $2$
Azam Hosseini
a.hosseini@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.
In this paper, the type-II matrices on (negative) Latin square graphs are considered and it is proved that, under certain conditions, the Nomura algebras of such type-II matrices are trivial. In addition, we construct type-II matrices on doubly regular tournaments and show that the Nomura algebras of such matrices are also trivial.
http://toc.ui.ac.ir/article_3002_619911c64aa82c9a4401803498c0f325.pdf
Doubly regular tournament
Nomura algebra
strongly regular graph
type-II matrix
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-09-01
2
3
13
19
3018
Two-out degree equitable domination in graphs
Ali Sahal
alisahl1980@gmail.com
1
Veena Mathad
veena mathad@rediffmail.com
2
University of mysore
University of Mysore
An equitable domination has interesting application in the context of social networks. In a network, nodes with nearly equal capacity may interact with each other in a better way. In the society persons with nearly equal status, tend to be friendly. In this paper, we introduce new variant of equitable domination of a graph. Basic properties and some interesting results have been obtained.
http://toc.ui.ac.ir/article_3018_9be4cc1a977118e5831a295b085d965d.pdf
Equitable Domination Number
Two-Out Degree
Minimal Two-Out Degree Equitable
Dominating set
Two-Out Degree Equitable Domatic Partition
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-09-01
2
3
21
32
3051
Bounding the rainbow domination number of a tree in terms of its annihilation number
Nasrin Dehgardi
ndehgardi@gmail.com
1
Mahmoud Sheikholeslami
s.m.sheikholeslami@azaruniv.edu
2
Abdollah Khodkar
akhodkar@westga.edu
3
Azarbaijan Shahid Madani University
Azarbaijan Shahid Madani University
University Of West Georgia
A $2$-rainbow dominating function (2RDF) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set ${1,2}$ such that for any vertex $vin V(G)$ with $f(v)=emptyset$ the condition $bigcup_{uin N(v)}f(u)={1,2}$ is fulfilled, where $N(v)$ is the open neighborhood of $v$. The weight of a 2RDF $f$ is the value $omega(f)=sum_{vin V}|f (v)|$. The $2$-rainbow domination number of a graph $G$, denoted by $gamma_{r2}(G)$, is the minimum weight of a 2RDF of 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 prove that for any tree $T$ with at least two vertices, $gamma_{r2}(T)le a(T)+1$.
http://toc.ui.ac.ir/article_3051_dc39b3b99937a3eea4c41cc51272e53a.pdf
annihilation number
2-rainbow dominating function
2-rainbow domination number
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-09-01
2
3
33
41
3277
On the unimodality of independence polynomial of certain classes of graphs
Saeid Alikhani
alikhani@yazd.ac.ir
1
Fatemeh Jafari
math_fateme@yahoo.com
2
Yazd University
Yazd university
The independence polynomial of a graph $G$ is the polynomial $sum i_kx^k$, where $i_k$ denote the number of independent sets of cardinality $k$ in $G$. In this paper we study unimodality problem for the independence polynomial of certain classes of graphs.
http://toc.ui.ac.ir/article_3277_694454b03718e08109baf2f20a978746.pdf
Independence polynomial
Unimodality
Log-concave
Polyphenyl hexagonal chains
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-09-01
2
3
43
52
3288
Note on degree Kirchhoff index of graphs
Mardjan Hakimi-Nezhaad
hakimi-nezhaad@kashanu.ac.ir
1
Ali Reza Ashrafi
ashrafi@kashanu.ac.ir
2
Ivan Gutman
gutman@kg.ac.rs
3
University of Kashan
University of Kashan
University of Kragujevac
Kragujevac, Serbia
The degree Kirchhoff index of a connected graph $G$ is defined as the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices, where $d_i$ is the degree of the $i$-th vertex, and $r_{ij}$ the resistance distance between the $i$-th and $j$-th vertex of $G$. Bounds for the degree Kirchhoff index of the line and para-line graphs are determined. The special case of regular graphs is analyzed.
http://toc.ui.ac.ir/article_3288_800dfa2ece27e5c09dd0f21f014c8dc9.pdf
resistance distance (in graphs)
Kirchhoff index
degree Kirchhoff index
spectrum of graph
Laplacian spectrum of graph
eng
University of Isfahan
Transactions on Combinatorics
2251-8657
2251-8665
2013-09-01
2
3
53
67
3292
Energy of binary labeled graphs
Pradeep Bhat
pg.bhat@manipal.edu
1
Sabitha D'Souza
sabithachetan@gmail.com
2
Manipal Institute of Technology
Manipal University
Manipal Institute of Technology, Manipal University
Let $G$ be a graph with vertex set $V(G)$ and edge set $X(G)$ and consider the set $A={0,1}$. A mapping $l:V(G)longrightarrow A$ is called binary vertex labeling of $G$ and $l(v)$ is called the label of the vertex $v$ under $l$. In this paper we introduce a new kind of graph energy for the binary labeled graph, the labeled graph energy $E_{l}(G)$. It depends on the underlying graph $G$ and on its binary labeling, upper and lower bounds for $E_{l}(G)$ are established. The labeled energies of a number of well known and much studied families of graphs are computed.
http://toc.ui.ac.ir/article_3292_782073aa78bf670706945d083a62986b.pdf
Label Matrix
Label Eigenvalues
Label Energy