and DISJOINT SETS:: {(yr,. ",!n¡2,2r,"',zntz) e N" I n is even and {Y""' '!n¡z\ ^ {2""''z'¡'\: Ø} on random access machines where the number of registers is bounded by an arbitrary function of n. nontrivial (i.e', superlinear) optimal lower bound on the computa problem on a random acc€ss machine' We will also show that (n log n) is relatively stable insofar"as it remains valid if we attach an a...

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the annihilating-ideal graph of a commutative ring $r$ is denoted by $ag(r)$, whose vertices are all nonzero ideals of $r$ with nonzero annihilators and two distinct vertices $i$ and $j$ are adjacent if and only if $ij=0$. in this article, we completely characterize rings $r$ when $gr(ag(r))neq 3$.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...

Abstract Violent coniflicts, particularly at election times in Africa, are a common cause of instability and economic disruption. This paper studies how firms react to electoral violence using the case Kenyan ower exporters during 2008 post-election as an example. The induced large negative supply shock that reduced exports primarily through workers' absence had heterogeneous effects: larger th...

As a joint development between Catalogue of Life (COL) and the Global Biodiversity Information Facility (GBIF), ChecklistBank supports publication curation checklists provides platform for their consistent discovery, use citation. GBIF has some time maintained as its repository community to share species checklist data drive searches on GBIF. The collaboration built an earlierversion, add funct...

The infl uence of vernalization temperature and duration and devernalization treatments on subsequent growth and fl ower development of Campanula ‘Birch Hybrid’ and Leucanthemum ×superbum Bergman ex J. Ingram ‘Snow Cap’ was determined. In the vernalization experiment, plants of ‘Birch Hybrid’ were vernalized at 0, 2.5, 5, 7.5, or 10 °C for 2, 4, 6, or 8 weeks. ‘Snow Cap’ was vernalized at 0, 2....