On the nomura algebras of formally self-dual association schemes of class $2$
Azam
Hosseini
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
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
3
no.
2013
1
11
http://toc.ui.ac.ir/article_3002_619911c64aa82c9a4401803498c0f325.pdf
dx.doi.org/10.22108/toc.2013.3002
Two-out degree equitable domination in graphs
Ali
Sahal
University of mysore
author
Veena
Mathad
University of Mysore
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
3
no.
2013
13
19
http://toc.ui.ac.ir/article_3018_9be4cc1a977118e5831a295b085d965d.pdf
dx.doi.org/10.22108/toc.2013.3018
Bounding the rainbow domination number of a tree in terms of its annihilation number
Nasrin
Dehgardi
Azarbaijan Shahid Madani University
author
Mahmoud
Sheikholeslami
Azarbaijan Shahid Madani University
author
Abdollah
Khodkar
University Of West Georgia
author
text
article
2013
eng
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 $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u\in N(v)}f(u)=\{1,2\}$ is fulfilled, where $N(v)$ is the open neighborhood of $v$. The weight of a 2RDF $f$ is the value $\omega(f)=\sum_{v\in V}|f (v)|$. 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, $\gamma_{r2}(T)\le a(T)+1$.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
3
no.
2013
21
32
http://toc.ui.ac.ir/article_3051_dc39b3b99937a3eea4c41cc51272e53a.pdf
dx.doi.org/10.22108/toc.2013.3051
On the unimodality of independence polynomial of certain classes of graphs
Saeid
Alikhani
Yazd University
author
Fatemeh
Jafari
Yazd university
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
3
no.
2013
33
41
http://toc.ui.ac.ir/article_3277_694454b03718e08109baf2f20a978746.pdf
dx.doi.org/10.22108/toc.2013.3277
Note on degree Kirchhoff index of graphs
Mardjan
Hakimi-Nezhaad
University of Kashan
author
Ali Reza
Ashrafi
University of Kashan
author
Ivan
Gutman
University of Kragujevac
Kragujevac, Serbia
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
3
no.
2013
43
52
http://toc.ui.ac.ir/article_3288_800dfa2ece27e5c09dd0f21f014c8dc9.pdf
dx.doi.org/10.22108/toc.2013.3288
Energy of binary labeled graphs
Pradeep
Bhat
Manipal Institute of Technology
Manipal University
author
Sabitha
D'Souza
Manipal Institute of Technology,
Manipal University
author
text
article
2013
eng
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.
Transactions on Combinatorics
University of Isfahan
2251-8657
2
v.
3
no.
2013
53
67
http://toc.ui.ac.ir/article_3292_782073aa78bf670706945d083a62986b.pdf
dx.doi.org/10.22108/toc.2013.3292