We prove that for any class of finite or countable graphs closed under taking subgraphs, and such that every finite graph in the class has a number of edges linearly bounded in terms of the number of vertices, the edge set quantifications can be replaced by vertex set quantifications in Monadic secondorder formulas. This result extends to hypergraphs of bounded rank.

A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.

In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...

Let C be the claw K 1;3 and N the net, i.e. the only connected graph with degree sequence 333111. It is known Bedrossian 1991; Faudree and Gould 1997] that if X; Y is a pair of connected graphs such that, for any 2-connected graph G, G being X Y-free implies G is hamiltonian, then X is the claw C and Y belongs to a nite list of graphs, one of them being the net N. For any such pair X; Y we show...

A conjecture by D. Seese states that if a set of graphs has a decidable monadic second-order theory, then it is the image of a set of trees under a transformation of relational structures defined by monadic second-order formulas, or equivalently, has bounded clique-width. We prove that this conjecture is true if and only if it is true for the particular cases of bipartite undirected graphs, of ...

Courcelle, B., The monadic second-order logic of graphs V: on closing the gap between definability and recognizability, Theoretical Computer Science 80 (1991) 153-202. Context-free graph-grammars are considered such that, in every generated graph (3, a derivation tree of G can be constructed by means of monadic second-order formulas that specify its nodes, its labels, the successors of a node e...

Effect of CO2-related acidification on aspects of the larval development of the European lobster, Homarus gammarus (L.) K. E. Arnold, H. S. Findlay, J. I. Spicer, C. L. Daniels, and D. Boothroyd National Lobster Hatchery, South Quay, Padstow, Cornwall, PL28 8BL, UK Plymouth Marine Laboratory, Prospect Place, West Hoe, Plymouth, Devon, PL1 3DH, UK Marine Biology and Ecology Research Centre, Scho...

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We prove that we can specify by formulas of monadic second-order logic the unique planar embedding of a 3-connected planar graph. If the planar graph is not 3-connected but given with a linear order of its set of edges, we can also define a planar embedding by monadic second-order formulas. We cannot do so in general without the ordering, even for 2-connected planar graphs. The planar embedding...

Betulonic acid belongs to the pentacyclic triterpenic derivative class and can be obtained through the selective oxidation of betulin. In this study we set obtaining several functionalized derivatives of this compound by its condensation with several amino compounds such as aminoguanidine, hydroxylamine, n-butylamine and thiosemicarbazide as our goal. The functionalization of the parent compoun...