@Article{Hosseini2013,
author="Hosseini, Azam
and Rahnamai Barghi, Amir",
title="On the nomura algebras of formally self-dual association schemes of class $2$",
journal="Transactions on Combinatorics",
year="2013",
volume="2",
number="3",
pages="1-11",
abstract="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.",
issn="2251-8657",
doi="10.22108/toc.2013.3002",
url="http://toc.ui.ac.ir/article_3002.html"
}
@Article{Sahal2013,
author="Sahal, Ali
and Mathad, Veena",
title="Two-out degree equitable domination in graphs",
journal="Transactions on Combinatorics",
year="2013",
volume="2",
number="3",
pages="13-19",
abstract="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.",
issn="2251-8657",
doi="10.22108/toc.2013.3018",
url="http://toc.ui.ac.ir/article_3018.html"
}
@Article{Dehgardi2013,
author="Dehgardi, Nasrin
and Sheikholeslami, Mahmoud
and Khodkar, Abdollah",
title="Bounding the rainbow domination number of a tree in terms of its annihilation number",
journal="Transactions on Combinatorics",
year="2013",
volume="2",
number="3",
pages="21-32",
abstract="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, $\gamma_{r2}(T)\le a(T)+1$.",
issn="2251-8657",
doi="10.22108/toc.2013.3051",
url="http://toc.ui.ac.ir/article_3051.html"
}
@Article{Alikhani2013,
author="Alikhani, Saeid
and Jafari, Fatemeh",
title="On the unimodality of independence polynomial of certain classes of graphs",
journal="Transactions on Combinatorics",
year="2013",
volume="2",
number="3",
pages="33-41",
abstract="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.",
issn="2251-8657",
doi="10.22108/toc.2013.3277",
url="http://toc.ui.ac.ir/article_3277.html"
}
@Article{Hakimi-Nezhaad2013,
author="Hakimi-Nezhaad, Mardjan
and Ashrafi, Ali Reza
and Gutman, Ivan",
title="Note on degree Kirchhoff index of graphs",
journal="Transactions on Combinatorics",
year="2013",
volume="2",
number="3",
pages="43-52",
abstract="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.",
issn="2251-8657",
doi="10.22108/toc.2013.3288",
url="http://toc.ui.ac.ir/article_3288.html"
}
@Article{Bhat2013,
author="Bhat, Pradeep G.
and D'Souza, Sabitha",
title="Energy of binary labeled graphs",
journal="Transactions on Combinatorics",
year="2013",
volume="2",
number="3",
pages="53-67",
abstract="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.",
issn="2251-8657",
doi="10.22108/toc.2013.3292",
url="http://toc.ui.ac.ir/article_3292.html"
}