A distinguishing r-labeling of a digraph G is a mapping λ from the set of vertices of G to the set of labels {1, . . . , r} such that no nontrivial automorphism of G preserves all the labels. The distinguishing number D(G) of G is then the smallest r for which G admits a distinguishing r-labeling. From a result of Gluck (David Gluck, Trivial set-stabilizers in finite permutation groups, Can. J....

In this issue, Estrada et al. (2003) provide new and important insights into how the endoplasmic reticulum (ER) of budding yeast cells is inherited. Together with other studies in plant and animal cells, the results of Estrada et al. (2003) support the idea that myosin V acts as a universal motor for the transport of ER membranes.

Patricia González-Cano1, Rommel Chacón-Salinas2, Victoria Ramos-Kichik2, Rogelio Hernández-Pando3, Jeanet Serafín-López2, Georgina Filio-Rodríguez2, Sergio Estrada-Parra2 and Iris Estrada-García2 1Vaccine and Infectious Disease Organization, University of Saskatchewan 2Escuela Nacional de Ciencias Biológicas, I.P.N., 3Instituto de Ciencias Médicas y de la Nutrición “Salvador Zubirán”, S.S. 1Can...

The atom-bond connectivity index—abbreviated ABC—has proven to describe the heat of formation of alkanes with an accuracy comparable to that of high-level ab initio and DFTmethods. Its physical interpretation in terms of quantumtheory, its generalization, and many of its mathematical properties have been reported. Here, a probabilistic interpretation of the generalized ABC index is provided. It...

SLEE has various applications in a large variety of problems. The signless Laplacian Estrada index hypergraph H is defined as SLEE(H)=∑i=1neλi(Q), where λ1(Q),λ2(Q),…,λn(Q) are the eigenvalues matrix H. In this paper, we characterize unique r-uniform unicyclic hypergraphs with maximum and minimum SLEE.

Although the bacterium Xanthomonas pruni utilizes the classic "tryptophan pathway" to synthesize nicotinic acid (Wilson and Henderson, J. Bacteriol. 85:221, 1963), evidence is accumulating that most bacteria do not exhibit a tryptophan-nicotinic acid relationship. The absence of such a relationship in Escherichia coli and Bacillus subtilis was reported by Yanofsky (J. Bacteriol. 68:577, 1954). ...