University of IsfahanTransactions on Combinatorics2251-86578320190901A lower bound on the $k$-conversion number of graphs of maximum degree $k+1$1122329910.22108/toc.2019.112258.1579ENChristina MynhardtDepartment of Mathematics and Statistics
University of VictoriaJane WodlingerDepartment of Mathematics and Statistics, University of VictoriaJournal Article20180726We derive a new sharp lower bound on the $k$-conversion number of graphs of maximum degree $k+1$. This generalizes a result of W.~Staton [Induced forests in cubic graphs, <em>Discrete Math.</em>,<strong>49</strong> (1984) 175--178], which established a lower bound on the $k$-conversion number of $(k+1)$-regular graphs.http://toc.ui.ac.ir/article_23299_8d28eb07589f4ea8b230f27577689a34.pdfUniversity of IsfahanTransactions on Combinatorics2251-86578320190901A note on fall colorings of Kneser graphs13152351010.22108/toc.2019.113909.1602ENSaeed ShaebaniSchool of Mathematics and Computer Science,
Damghan University,
P.O. Box 36716-41167, Damghan, IranJournal Article20181110A fall coloring of a graph $G$ is a proper coloring of $G$ with $k$ colors such that each vertex sees all $k$ colors on its closed neighborhood. In this paper, we characterize all fall colorings of Kneser graphs of type $KG(n,2)$.http://toc.ui.ac.ir/article_23510_458e3ee1f3eb690f420775ecd2f2dcc0.pdfUniversity of IsfahanTransactions on Combinatorics2251-86578320190901A note on full weight spectrum codes15222351210.22108/toc.2019.112621.1584ENTim AldersonUniversity of New Brunswick0000-0002-7608-5122Journal Article20180821A linear $ [n,k]_q $ code $ C $ is said to be a full weight spectrum (FWS) code if there exist codewords of each weight less than or equal to $ n $. In this brief communication we determine necessary and sufficient conditions for the existence of linear $ [n,k]_q $ full weight spectrum (FWS) codes. Central to our approach is the geometric view of linear codes, whereby columns of a generator matrix correspond to points in $ PG(k-1,q) $.http://toc.ui.ac.ir/article_23512_462e33ca7b1dc1707d553e38ec31ab59.pdfUniversity of IsfahanTransactions on Combinatorics2251-86578320190901A generalization of Hall's theorem for $k$-uniform $k$-partite hypergraphs23282362410.22108/toc.2019.105022.1506ENReza Jafarpour-GolzariDepartment of Mathematics, Institute for Advanced Studies in Basic Science (IASBS), Zanjan, IranJournal Article20170627In this paper we prove a generalized version of Hall's theorem in graphs, for hypergraphs. More precisely, let $mathcal{H}$ be a $k$-uniform $k$-partite hypergraph with some ordering on parts as $V_{1}, V_{2},ldots,V_{k}$ such that the subhypergraph generated on $bigcup_{i=1}^{k-1}V_{i}$ has a unique perfect matching. In this case, we give a necessary and sufficient condition for having a matching of size $t=|V_{1}|$ in $mathcal{H}$. Some relevant results and counterexamples are given as well.http://toc.ui.ac.ir/article_23624_85349dfacd04742bbd3b32ade012d578.pdfUniversity of IsfahanTransactions on Combinatorics2251-86578320190901On the first and second Zagreb indices of quasi unicyclic graphs29392386010.22108/toc.2019.115147.1615ENMajid AghelFerdowsi University of Mashhad, International CampusAhmad ErfanianFerdowsi University0000-0002-9637-1417Ali Reza AshrafiUniversity of KashanJournal Article20190117Let $G$ be a simple graph. The graph $G$ is called a quasi unicyclic graph if there exists a vertex $x in V(G)$ such that $G-x$ is a connected graph with a unique cycle. Moreover, the first and the second Zagreb indices of $G$ denoted by $M_1(G)$ and $M_2(G)$, are the sum of $deg^2(u)$ overall vertices $u$ in $G$ and the sum of $deg(u)deg(v)$ of all edges $uv$ of $G$, respectively. The first and the second Zagreb indices are defined relative to the degree of vertices. In this paper, sharp upper and lower bounds for the first and the second Zagreb indices of quasi unicyclic graphs are given.http://toc.ui.ac.ir/article_23860_e581b89bf87f7982b092368e44158c2d.pdf