Symmetric binary Steinhaus triangles and parity-regular Steinhaus graphs

A binary Steinhaus triangle is a of zeroes and ones that points down with the same local rule as Pascal modulo 2. said to be rotationally symmetric, horizontally symmetric or dihedrally if it invariant under 120 degrees rotation, horizontal reflection both, respectively. The first part this paper devoted study linear subspaces triangles. We obtain simple explicit bases for each them by using elementary properties binomial coefficients. graph an adjacency matrix whose upper-triangular triangle. even odd all its vertex are odd, One main results existence isomorphism between subspace graphs certain This permits us give, in second paper, basis vector space parity-regular graphs; i.e., odd. Finally, last we consider generalized triangles, triangles ones, point up now, always New deduced from part.