We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval-valued fuzzy complete graphs.

A graph is connected-homogeneous if any isomorphism between finite connected induced subgraphs extends to an automorphism of the graph. In this paper we classify the countably infinite connectedhomogeneous graphs. We prove that if Γ is connected countably infinite and connected-homogeneous then Γ is isomorphic to one of: Lachlan and Woodrow’s ultrahomogeneous graphs; the generic bipartite graph...

The boxicity box(H) of a graph H is the smallest integer d such that H is the intersection of d interval graphs, or equivalently, that H is the intersection graph of axis-aligned boxes in R. These intersection representations can be interpreted as covering representations of the complement H of H with co-interval graphs, that is, complements of interval graphs. We follow the recent framework of...

we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $...

For given finite (unordered) graphs G and H, we examine the existence of a Ramsey graph F for which the strong Ramsey arrow F −→ (G)r holds. We concentrate on the situation when H is not a complete graph. The set of graphs G for which there exists an F satisfying F −→ (G)2 2 (P2 is a path on 3 vertices) is found to be the union of the set of chordal comparability graphs together with the set of...

This paper considers representations of graphs as rectangle-visibility graphs and as doubly linear graphs. These are, respectively, graphs whose vertices are isothetic rectangles in the plane with adjacency determined by horizontal and vertical visibility, and graphs that can be drawn as the union of two straight-edged planar graphs. We prove that these graphs have, with n vertices, at most 6n−...

In this paper we introduce and study an algebra of languages representable by vertex-labeled graphs. The proposed algebra is equipped with three operations: the union of languages, the merging of languages and the iteration. In contrast to Kleene algebra, which is mainly used for edge-labeled graphs, it can adequately represent many properties of languages defined by vertex-labeled graphs and p...