## Excursions in graph theory |

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2n+l adjacency matrix chromatic polynomial combinatorial design complete bipartite graph complete graph complete the proof component of G conjecture connected component connected graph construction cubic graphs DEFINITION deg(v deg(w degree sequence Dick Wick Hall double triangle edges in G edges of G EULER'S FORMULA Euler's problem eulerian circuit eulerian trail example EXCURSION FIGURE l0 find the arrangement follows forcibly hamiltonian G is connected Gardner Mathematical graph G graph theory graphical sequence hamiltonian cycle homeomorphic imbedding integer labelled Latin square Let G longest path loops Math matic polynomials Monthly 80 multiple edges n-regular necessary and sufficient number of edges number of vertices orthogonal l-factorizations pair of elements planar graph planar triangulation plane Posa's theorem procedure prove q edges reader regions result Room square Scientific American simple triangulation sphere square of side STS of order sufficient conditions tion tree triples vertex of G VII Amer W. T. Tutte