## Exploring graph theory, Volume 1 |

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6raph active vertex adjacent vertices algorithm binary tree block called Cayley's Cayley's theorem centre complement complete bipartite graph complete graph components conjecture connected graph Consider construct contains C4 corresponding cube cubic graphs cut-edge cut-vertex cut-vertices defined degree sequence deleted diagonals dots draw eccentricity edge incident edge-connectivity example follows frequency partition graph of fig graph theory hexagon hexominoes induction integers Investigate isolated vertices isomorphic labelled tree lines matched matrix maximum number mono triangles monochromatic triangle multigraph n-1 edges n-1 vertices n-gon non-adjacent vertices number of edges number of spanning number of vertices obtained pair of vertices path planted trivalent trees player polygon possible problem proof Prooi Prove result root Schlegel diagram single vertex six vertices spanning tree special graphs star graph subgraph subset switched symbol terminal vertices Theorem thrackle total number tree of fig two-tree unique vertex adjacent vertex connectivity vertex v3 vertices of degree