A successful heuristic algorithm for nding Hamilton cycles in cubic graphs is described Several graphs from The Foster census of connected symmetric trivalent graphs and all cubic Cayley graphs of the group PSL are shown to be hamiltonian Proposed running head HAMILTON CYCLES IN CUBIC GRAPHS

We explore ways to concisely describe circulant graphs, highly symmetric graphs with properties that are easier to generalize than other graphs. We introduce connection sets as a way to describe isomorphism among some circulant graphs and discuss Ádám’s conjecture that attempts to generalize this idea to all circulant graphs, exploring cases in which the conjecture holds and cases in which it f...

Exterior algebraic shifting and symmetric algebraic shifting of bipartite graphs and chordal graphs are studied in the present paper. keywords : Algebraic shifting, chordal graph.

This paper presents a new approach for intuitive and effective design of periodic symmetric tiles. We observe that planar graphs can effectively represent symmetric tiles and graph drawing provides an intuitive paradigm for designing symmetric tiles. Moreover, based on our theoretical work to represent hexagonal symmetry by rectangular symmetry, we are able to present all symmetric tiles as gra...

This paper presents a new approach for intuitive and effective design of periodic symmetric tiles. We observe that planar graphs can effectively represent symmetric tiles and graph drawing provides an intuitive paradigm for designing symmetric tiles. Moreover, based on our theoretical work to represent hexagonal symmetry by rectangular symmetry, we are able to present all symmetric tiles as gra...

This article presents some interesting properties about a new type of graph associated to a group, the G-graphs [4]. We show that many properties of a group can be seen on its associated G-graph and that many common graphs are G-graphs. We explain how to build efficiently some symmetric and semisymmetric graphs using the G-graphs. We establish a link beetwen Cayley graphs [1,2] and G-graphs.

Dedicated by the other authors to Professor John Maybee on the occasion of his 65th birthday. Abstract. One of the intriguing open problems on competition graphs is determining what digraphs have interval competition graphs. This problem originated in the work of Cohen 5, 6] on food webs. In this paper we consider this problem for the class of loopless symmetric digraphs. The competition graph ...

An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter of a tree T) is related to the maximum multiplicity occurring for an eigenvalue of a symmetric matrix whose graph is T (resp. the minimum number q(T) of distinct eigenvalues over the symmetric matr...

The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly’s and Mac Lane’s coherence theorem for symmetric monoidal closed categories. A coherence theorem with respect to these graphs is proved for proof-net categories. Such a coherence ...