When G is a rooted graph where each edge may independently succeed with probability p, we consider the expected number of vertices in the operational component of G containing the root. This expected value EV (G;p) is a polynomial in p. We present several distinct equivalent formulations of EV (G;p), unifying prior treatments of this topic. We use results on network resilience (introduced by Co...

For a rooted graph G, let EVb(G; p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We determine the expected value of EVb(G; p) for random trees, and include a connection to unrooted trees. We also consider rooted digraphs, computing the expected value of a random orientation of a rooted graph G in terms of E...

For a rooted graph G, let EV (G; p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We examine combinatorial properties of this polynomial, proving that G is k-edge connected iff EV ′(G; 1) = · · · = EV k−1(G; 1) = 0. We find bounds on the first and second derivatives of EV (G; p); applications yield character...

The present work describes an efficient micropropagation and callus induction protocol of Limbarda crithmoïdes L. (Asteraceae), a halophyte species with medicinal horticultural interests. objective was to identify the culture media that support best organogenesis callogenic expressions four types aerial explants; nodal internodal segments leaf portions, by varying mineral composition twenty add...

Perception of microbial signal molecules is part of the strategy evolved by plants to survive attacks by potential pathogens. To gain a more complete understanding of the early signaling events involved in these responses, we used fungal components of Fusarium under in vitro condition and checked the rise in signal molecule, salicylic acid (SA), and marker enzymes in defense reactions against t...

The present study was undertaken to investigate the role of banana extract (BE) on synchronous plantlet formation from seeds of Dendrobium lituiflorum Lindl. The seedlings formed on modified Knudson C (KC) medium supplemented with 20% (v/v) BE had significantly high fresh and dry weights. Morphologically uniform plantlets with elongated leaves and well developed roots were formed on KC medium w...

DOG(R)1, which encodes 2-deoxyglucose-6-phosphate phosphatase, has been used as a selectable marker gene to produce transgenic plants. In this study, a transformation vector, pBIDOG, which contains the DOG(R)1 gene, was transformed into oil palm embryogenic calli (EC) mediated by Agrobacterium tumefaciens strain LBA4404. Transformed EC were exposed to 400 mg l(-1) 2-deoxyglucose (2-DOG) as the ...

A method has been developed for plant regeneration by encapsulation of somatic embryos obtained from callus cultures derived from semi-mature cotyledon explants of Dalbergia sissoo Roxb. (family Fabaceae). Embryogenic callus was developed from cotyledon pieces on Murashige and Skoog (1962) medium supplemented with 9.04 μM 2,4dichlorophenoxyacetic acid and 0.46 μM kinetin. The somatic embryos we...

For finite q, we classify the countable, descendant-homogeneous digraphs in which the descendant set of any vertex is a q-valent tree. We also give conditions on a rooted digraph Γ which allow us to construct a countable descendant-homogeneous digraph in which the descendant set of any vertex is isomorphic to Γ. 2010 Mathematics Subject Classification: 05C20, 05C38, 20B27