walk, finite alternating sequence of vertices and edges, beginning and ending with vertices. No edge appears more than once., path, An open walk in which no vertex appears more than once, circuit, A closed walk in which no vertex appears more than once., handshaking theorem, sum of the degrees of the vertices of a graph is twice the number of edges., Hamiltonian circuit, closed walk that traverses every vertex of graph G exactly once except starting and terminal vertex., Simple graph, A graph in which each edge connects two different vertices and where no two edges connect the same pair of vertices., Multigraph, A graph in which multiple edges may connect the same pair of vertices., Complete Graph, graph of n vertices having exactly one edge between each pair of vertices., Tree, graph that is connected and has no cycles., Euler Graph, A connected graph G in which there is a closed trail which includes every edge of the graph G., Hamiltonian Graph, A connected graph G in which there is a cycle which includes every vertex of G., Regular Graph, A graph in which all the vertices have the same degree..

Graph Theory

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