A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős–Ko–Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corres...

let $g$ be a simple graph of order $n$ and size $m$.the edge covering of $g$ is a set of edges such that every vertex of $g$ is incident to at least one edge of the set. the edge cover polynomial of $g$ is the polynomial$e(g,x)=sum_{i=rho(g)}^{m} e(g,i) x^{i}$,where $e(g,i)$ is the number of edge coverings of $g$ of size $i$, and$rho(g)$ is the edge covering number of $g$. in this paper we stud...

a recursive-circulant $g(n; d)$ is defined to be acirculant graph with $n$ vertices and jumps of powers of $d$.$g(n; d)$ is vertex-transitive, and has some strong hamiltonianproperties. $g(n; d)$ has a recursive structure when $n = cd^m$,$1 leq c < d $ [10]. in this paper, we will find the automorphismgroup of some classes of recursive-circulant graphs. in particular, wewill find that the autom...

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

in this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. weobserve that over a commutative ring $r$, $bbb{ag}_*(_rm)$ isconnected and diam$bbb{ag}_*(_rm)leq 3$. moreover, if $bbb{ag}_*(_rm)$ contains a cycle, then $mbox{gr}bbb{ag}_*(_rm)leq 4$. also for an $r$-module $m$ with$bbb{a}_*(m)neq s(m)setminus {0}$, $...

An investigation of the estimation of leaf biochemistry in open tree crop canopies using high-spatial hyperspectral remote sensing imagery is presented. Hyperspectral optical indices related to leaf chlorophyll content were used to test different radiative transfer modelling assumptions in open canopies where crown, soil and shadow components were separately targeted using 1 m spatial resolutio...

let $g=(v,e)$ be a‎ ‎simple graph of order $n$ and size $m$‎. ‎an $r$-matching of $g$ is ‎a set of $r$ edges of $g$ which no two of them have common vertex‎. ‎the hosoya index $z(g)$ of a graph $g$ is defined as the total‎ ‎number of its matchings‎. ‎an independent set of $g$ is a set of‎ ‎vertices where no two vertices are adjacent‎. ‎the ‎merrifield-simmons index of $g$ is defined as the tota...