University of IsfahanTransactions on Combinatorics2251-86572320130901On the nomura algebras of formally self-dual association schemes of class $2$111300210.22108/toc.2013.3002ENAzamHosseiniDepartment of Mathematics,
K. N. Toosi University of TechnologyAmirRahnamai BarghiK. N. Toosi university of Technology University, Tehran-Iran.Journal Article20130521In this paper, the type-<em>II</em> matrices on (negative) Latin square graphs are considered and it is proved that, under certain conditions, the Nomura algebras of such type<em>-II</em> matrices are trivial. In addition, we construct type-<em>II</em> matrices on doubly regular tournaments and show that the Nomura algebras of such matrices are also trivial.https://toc.ui.ac.ir/article_3002_619911c64aa82c9a4401803498c0f325.pdfUniversity of IsfahanTransactions on Combinatorics2251-86572320130901Two-out degree equitable domination in graphs1319301810.22108/toc.2013.3018ENAliSahalUniversity of mysoreVeenaMathadUniversity of MysoreJournal Article20130202An 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.https://toc.ui.ac.ir/article_3018_9be4cc1a977118e5831a295b085d965d.pdfUniversity of IsfahanTransactions on Combinatorics2251-86572320130901Bounding the rainbow domination number of a tree in terms of its annihilation number2132305110.22108/toc.2013.3051ENNasrinDehgardiAzarbaijan Shahid Madani UniversityMahmoudSheikholeslamiAzarbaijan Shahid Madani UniversityAbdollahKhodkarUniversity Of West GeorgiaJournal Article20130130A <em>$2$-rainbow dominating function</em> (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 <em>weight</em> of a 2RDF $f$ is the value $\omega(f)=\sum_{v\in V}|f (v)|$. The <em>$2$-rainbow domination number</em> of a graph $G$, denoted by $\gamma_{r2}(G)$, is the minimum weight of a 2RDF of G.
The <em>annihilation number</em> $a(G)$ 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, $\gamma_{r2}(T)\le a(T)+1$.https://toc.ui.ac.ir/article_3051_dc39b3b99937a3eea4c41cc51272e53a.pdfUniversity of IsfahanTransactions on Combinatorics2251-86572320130901On the unimodality of independence polynomial of certain classes of graphs3341327710.22108/toc.2013.3277ENSaeidAlikhaniYazd UniversityFatemehJafariYazd universityJournal Article20121103The 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.https://toc.ui.ac.ir/article_3277_694454b03718e08109baf2f20a978746.pdfUniversity of IsfahanTransactions on Combinatorics2251-86572320130901Note on degree Kirchhoff index of graphs4352328810.22108/toc.2013.3288ENMardjanHakimi-NezhaadUniversity of KashanAli RezaAshrafiUniversity of KashanIvanGutmanUniversity of Kragujevac
Kragujevac, SerbiaJournal Article20130712The 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.https://toc.ui.ac.ir/article_3288_800dfa2ece27e5c09dd0f21f014c8dc9.pdfUniversity of IsfahanTransactions on Combinatorics2251-86572320130901Energy of binary labeled graphs5367329210.22108/toc.2013.3292ENPradeep G.BhatManipal Institute of Technology
Manipal UniversitySabithaD'SouzaManipal Institute of Technology,
Manipal UniversityJournal Article20130712Let $G$ 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.https://toc.ui.ac.ir/article_3292_782073aa78bf670706945d083a62986b.pdf