Vocab associated with trees
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| Graph | A graph G is a collection of two sets: V, a set of vertices and E, a set of edges that connect the vertices
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| Digraph | {v1, v2} - graph in which each edge is associated with an ordered pair of vertices
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| Undirected Graph | graph in which each edge is associated with an unordered pair of vertices
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| Adjacent | a vertex v1 in a graph G is adjacent to v2 if there is an edge between v1 to v2
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| Path | sequence of vertices v1, v2, v3,...vn where there is an edge from vi to vi+1
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| Simple Path | path in which all vertices are distinct
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| Cycle | a path in which first and last vertices are the same
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| Simple Cycle | a cycle that begins and ends at the same vertex and does not pass through other vertices more than once
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| Acyclic Graph | graph with no cycles
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| Tree | connected, acyclic graph with a specially designated vertex called the root
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| Connected Graph | there is a path between any two vertices (undirected)
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| Strongly Connected Graph | there is a path between any two vertices (digraph)
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| Weakly Connected Graph | there is a path from vertex I to vertex J or from vertex J to vertex I
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| Complete Graph | a graph with each pair of distinct vertices having an edge between them (graph with n vertices and exactly n(n-1)/2 edges)
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| Complete Directed Graph | a directed graph with exactly n(n-1) edges
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| Multigraph | figure which has multiple occurrences of the same edge (two or more edges between two vertices)
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| Network | graph in which each edge has an associated positive numerical weight
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| Topological Order | linear ordering of the vertices in a digraph in which vertex x precedes vertex y if there is a directed edge from x to y in the graph
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| Spanning Tree | a subgraph of a connected undirected graph that contains all of its vertices and enough of its edges to form a tree
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| DFS Spanning Tree | spanning tree created by executing a depth-first search of a graph's vertices
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| Minimal Spanning Tree | spanning tree of a weighted, connected, undirected graph which has minimal edge-weight sum
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| Euler Circuit | a path in an undirected graph that begins at a vertex v, passes through every edge in the graph exactly once, and terminates at v
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| Hamilton Circuit | a path that begins at a vertex v, passes through every vertex in the graph exactly once, and terminates at v.
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| Traveling Salesman Problem | A weighted digraph must be traversed with minimal cost. It is in the set NP; the solution can be guessed and then checked in polynomial time. It is also NPC.
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| Four Color Problem | Since the proving of the theorem, efficient algorithms have been found for 4-coloring maps requiring only O(n^2) time, where n is the number of vertices, found in 1996
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| Three Utility Problem |
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