Abstract. A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial graph. ...

See examples in Fig. 1(b). Many graph algorithms use an st-orientation. For instance, graph drawing algorithms [3], [4], [17], [19], [22], routing algorithms [1], [13] and partitioning algorithms [14]. Given a biconnected graph G and its two vertices s and t, one can find an st-orientation of G in O(m + n) time [5], [6], [22]. Note that if G is not biconnected then G may have no st-orientation....

A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are minimal with this property. 2009 Wiley Periodicals, Inc. J Graph Theory 62: 369–384, 2009

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...