On R -hued Coloring Of K_2,3 -minor Free Graphs And Computer Search Of Isospectral Polyominoes

In this paper, we study the r-hued coloring of K2,3-minor free graphs and computer search of isopectral polyominoes. the r-hued coloring of a graph is natural extend of normal coloring, but between them also have many difference. By the structure definition of the K2,3-minor free graph, we study the r-hued coloring of the outplanar graphs at first. And then, we study the r-hued coloring of the K2,3-minor free graphs. We obtain the result that for any K2,3-minor free graph G, Xr(G)≤r+3, XL,r(G)≤r+4.A polyomino (graph) is a finite 2-connected graph of regular squares such that any two squares have exactly one common edge or are disjoint. Since the information of each graph need to be recorded during constructive enumerating, we propose a new code for polyominoes, binary 2-dimentional code(B2DC), in this paper. Then we propose an algorithm to build adjacent matrices and laplacian matrices by B2DCs of polyominoes. We searched a pair of minimum iso-Laplacian-spectral polyomino graphs by computing characteristic polynomials of those matrices.