فهرست مطالب

  • Volume:8 Issue:3, 2019
  • تاریخ انتشار: 1398/06/10
  • تعداد عناوین: 5
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  • Christina Mynhardt, Jane Wodlinger * Pages 1-12
    ‎‎We 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, ‎Discrete Math.‎,49 (‎1984) ‎175--178‎]‎, ‎which established a lower bound on the $k$-conversion number of $(k+1)$-regular graphs‎.
    Keywords: irreversible k-threshold conversion process, network diffusion process, conversion number, conversion set
  • Saeed Shaebani * Pages 13-15
    A 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 $KG(n,2)$‎.
    Keywords: Kneser graph‎, ‎fall coloring‎, ‎b-coloring
  • Tim Alderson * Pages 15-22
    A 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) $.
    Keywords: weight spectrum, linear code, Hamming weight, FWS, MWS
  • Reza Jafarpour, Golzari * Pages 23-28
    In 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.
    Keywords: $k$-uniform $k$-partite hypergraph‎, ‎matching‎, ‎perfect matching‎, ‎vertex cover‎, ‎Hall&#039, s theorem
  • Majid Aghel, Ahmad Erfanian *, Ali Reza Ashrafi Pages 29-39
    ‎Let $G$ 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.
    Keywords: ‎First Zagreb index‎, Second Zagreb index‎, Quasi Unicyclic graphs