## Fundamentals of graph theory |

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adjacency matrix algorithm arbitrary arcs Berge graph bicomponents biconnected block called chromatic number clique columns common vertex condition conjecture connected graph consider construct contains corresponding cutpoint cyclomatic dichain dicycle digraph G distinct vertices edge coloring elements equivalent Eulerian cycle example Exer F.Harary finite G and G graph G graph in Figure graph theory Hamiltonian cycle Harary's book Hence homeomorphic incidence matrix incident invariant isomorphism J.Gr.Th joining kernel Lemma lf G lntroduction loops Math maximal metric multigraph n-vertex graph No.l nonadjacent vertices nonempty number of edges number of vertices obtained from G odd length original graph pairwise partial G perfect graph planar graph polynomial possible problem proof Prove quasicycle removal satisfies set of vertices simple chain simple cutset simple cycle simple graph smallest number subgraph subgraph G subset Suppose Theorem topological transitive triangulation unique vertex coloring vertices of G walk