In this paper we study a new product of graphs called tight product. A graph H is said to be a tight product of two (undirected multi) graphs G1 and G2, if V (H) = V (G1) × V (G2) and both projection maps V (H) → V (G1) and V (H) → V (G2) are covering maps. It is not a priori clear when two given graphs have a tight product (in fact, it is NP -hard to decide). We investigate the conditions unde...

What is the maximum possible number, f3(n), of vectors of length n over {0, 1, 2} such that the Hamming distance between every two is even? What is the maximum possible number, g3(n), of vectors in {0, 1, 2}n such that the Hamming distance between every two is odd? We investigate these questions, and more general ones, by studying Xor powers of graphs, focusing on their independence number and ...

In 1891, Peterson [6] proved that every 3-regular bridge-less graph has a perfect matching. It is well known that the dual of a triangular mesh on a compact manifold is a 3-regular graph. M. Gopi and D. Eppstein [4] use Peterson’s theorem to solve the problem of constructing strips of triangles from triangular meshes on a compact manifold. P. Diaz-Gutierrez and M. Gopi [3] elaborate on the crea...

Let G,H be graphs and G?H represent a particular graph product of G H. We define im(G) to the largest t such that has Kt-immersion ask: given im(G)=t im(H)=r, how large is im(G?H)? Best possible lower bounds are provided when ? Cartesian or lexicographic product, conjecture offered for each direct strong products, along with some partial results.