let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defi ned by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

Although the general problem of subgraph isomorphismis NP-complete, polynomial-time algorithms exist for recognizing any xed subgraph. However, certain subgraphs appear easier to recognize than others. In this paper, we present general algorithms for xed-subgraph isomorphism which improve or unify previous results. In particular, we present an O(n f m) algorithm for recognizing a xed subgraph H...

Broccoli (Brassica oleracea L. var. italica Plenck) and caulifl ower (B. oleracea var. botrytis DC) are closely related botanical varieties. The underlying genetic bases of their phenotypic differences from each other are not well understood. A molecular genetic marker enabling B. oleracea germplasm curators and breeders to predict phenotype from seeds or seedlings would be a valuable tool. Mut...

The aim of this study was to examine the environmental regulation of ̄ower initiation and subsequent development in heliotrope (Heliotropium aborescens L. cv. Marine). Five experiments were conducted, two examined whether ̄owering could be advanced by cool temperatures. The duration of cool temperature required to induce rapid ̄owering was also investigated. The ®nal three experiments examined ...

During the monitoring of populations of Anemone sylvestris L. (Ranunculaceae), a protected species in Poland, we found that the seed set is impaired. The fl ower is considered an adaptation that has coevolved to achieve effective pollination and successful fertilization. Therefore we have focused on the morphological and anatomical characteristics of the fl owers of A. sylvestris L. as a prelud...

Lysimeter experiments were conducted on rice during rainy season (July±October) and sun ̄ower during summer seasons (March±June) in a set of two electronic weighing type lysimeters of 2 m 2 m 2 m size to measure the hourly evapotranspiration of these crops from 1994 to 1995 at Karnal, India. The average weekly ET of rice varied from <3 mm per day in the early growing period to >6.6 mm per day at...

Characterization of saffl ower (Carthamus tinctorius L.) with molecular markers is needed to enhance germplasm management and utilization. Amplifi ed fragment length polymorphism (AFLP) analysis was completed in saffl ower resulting in 102 unambiguous polymorphic markers. Pairwise distances were calculated for eight diverse populations of 12 plants each, and on bulked leaf tissue of 96 accessio...

Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices: For 5 s m=4, a monotone circuit computing CLIQUE(m; s) contains at least (1=2)1:8 min( p s 1=2;m=(4s)) gates: If a non-monotone circuit computes CLIQUE using a \small" amount of negation,...