Glutamine synthetase (GS) is a key enzyme in nitrogen (N) assimilation, particularly during seed development. Three cytosolic GS isoforms (HvGS1) were identified in barley (Hordeum vulgare L. cvâ€¦ (More)

Interpretations for evaluations of the Tutte polynomial T (G;x, y) of a graph G are given at a number of points on the hyperbolae Hq = {(x, y) | (x âˆ’ 1)(y âˆ’ 1) = q}, for q a positive integer â€” pointsâ€¦ (More)

We introduce a newproperty of graphs called â€˜q-state Potts uniquenessâ€™ and relate it to chromatic and Tutte uniqueness, and also to â€˜chromaticâ€“flowuniquenessâ€™, recently studiedbyDuan,WuandYu. Weâ€¦ (More)

We prove that the problem of counting the number of colourings of the vertices of a graph with at most two colours, such that the colour classes induce connected subgraphs is #P-complete. We alsoâ€¦ (More)

The number of homomorphisms hom(G, Kk) from a graph G to the complete graph Kk is the value of the chromatic polynomial of G at a positive integer k. This motivates the following (cf. [3]):â€¦ (More)

J. Makowsky and B. Zilber (2004) showed that many variations of graph colorings, called CP-colorings in the sequel, give rise to graph polynomials. This is true in particular for harmoniousâ€¦ (More)

C. Merino proved recently the following identity between evaluations of the Tutte polynomial of complete graphs: t(Kn+2; 1,âˆ’1) = t(Kn; 2,âˆ’1). In this work we extend this result by giving a largeâ€¦ (More)

For integer q â‰¥ 2, we derive edge q-colouring models for (i) the Tutte polynomial of a graph G on the hyperbola H q , (ii) the symmetric weight enumerator for group-valued q-flows of G, and (iii) aâ€¦ (More)