1,720,986 research outputs found
1-factorisation of the Composition of Regular Graphs
No full text1-factorability of the composition of graphs is studied. The followings sufficient conditions are proved: is 1-factorable if and are regular and at least one of the following holds: (i) Graphs and both contain a 1-factor, (ii) is 1-factorable (iii) is 1-factorable. It is also shown that the tensor product is 1-factorable, if at least one of two graphs is 1-factorable. This result in turn implies that the strong tensor product is 1-factorable, if is 1-factorable
Molecular Graph Eigenvectors for Molecular Coordinates
No full textThis volume constitutes the proceedings of the DIMACS International Workshop on Graph Drawing, GD '94, held in Princeton, New Jersey in October 1994. The 50 papers and system descriptions presented address the problem of constructing geometric representations of abstract graphs, networks and hypergraphs, with applications to key technologies such as software engineering, databases, visual interfaces, and circuit layout; they are organized in sections on three-dimensional drawings, orthogonal drawings, planar drawings, crossings, applications and systems, geometry, system demonstrations, upward drawings, proximity drawings, declarative and other approaches; in addition reports on a graph drawing contest and a poster gallery are included
Search for Minimal Trivalent Cycle Permutation Graphs with Girth Nine
No full textThe question of the girth of cycle permutation graphs is discussed. It is demonstrated by a computer search, that there are no cycle permutation graphs with girth 9 on less than 60 vertices, and that precisely two non-isomorphic examples exist on 60 vertices
Edge-Colorability of Graph Bundles
No full textAbstractThe topological notion of a fibre bundle is a generalization both of a Cartesian product and of a covering space. A graph bundle is a combinatorial analog of a fibre bundle. Accordingly, it is a generalization both of a Cartesian product of two graphs and of a covering graph. A “total graph”X is formed from a “base graph”B and “fibre”F. The edge-colorability ofX is studied in terms ofB andF. In particular, it is proved that if a graph bundle with baseB and fibreF satisfies at least one of the conditions:(i)B is of chromatic class 1 andΔ(B) > 0, or(ii)F is of chromatic class 1 andΔ(F) > 0, or(iii)B andF both contain a 1-factor, then its total graphX is of chromatic class 1
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