We prove that if G and H are primitive strongly regular graphs with the same parameters and φ is a homomorphism from G to H, then φ is either an isomorphism or a coloring (homomorphism to a complete subgraph). Moreover, any such coloring is optimal for G and its image is a maximum clique of H. Therefore, the only endomorphisms of a primitive strongly regular graph are automorphisms or colorings...

For an integer k > 0, a graph G is k-triangular if every edge of G lies in at least k distinct 3-cycles of G. In [J. Graph Theory, 11 (1987), 399-407], Broersma and Veldman proposed an open problem: For a given positive integer k, determine the value s for which the statement Let G be a k-triangular graph. Then L(G), the line graph of G, is s-hamiltonian if and only L(G) is (s + 2)-connected is...

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...

In this work, simulations with scalene triangle meshes represented by a recently proposed graphbased adaptive mesh refinement technique are described. Previously, simulations exclusively with isosceles right triangles were presented with this graph-based scheme. This data structure represents triangular meshes in finite-volume discretizations in order to solve second-order partial differential ...

In this paper, we attach several new invariants to connected strongly regular graphs (excepting conference on non-square number of vertices): one invariant called the discriminant, and a p-adic corresponding each prime p. We prove parametric restrictions quasi-symmetric 2-designs with given block graph G defect (absolute difference two intersection numbers) solely in terms parameters G, includi...

In this paper we present an approximation algorithm for solving the following optimal motion planning problem: Given a planar space composed of triangular regions , each of which is associated with a positive unit weight, and two points s and t, nd a path from s to t with the minimum weight, where the weight of a path is deened to be the weighted sum of the lengths of the sub-paths within each ...

The structure of graded triangular algebras T of arbitrary dimension are studied in this paper. This is motivated in part for the important role that triangular algebras play in the study of oriented graphs, upper triangular matrix algebras or nest algebras. It is shown that T decomposes as T = U + ( ∑ i∈I Ti), where U is an R-submodule contained in the 0-homogeneous component and any Ti a well...