Math 100 Midterm 2026 Updated 2026

Math 100 Midterm 2026 Updated 2026 | A+ Graded Solutions Graph - answer - set of vertices and set of edges, represented as a set of pairs of vertices Complete Graph - answer - A graph in which every pair of vertices is joined by an edge exactly once. Simple Graph - answer - Has no loops and is not a multigraph. Order - answer - The order of G is the number of vertices in G. Size - answer - The size of G is the number of edges in G. Adjacent - answer - Two vertices (u and v) are adjacent if the graph contains an edge uv, joining the vertices u and v Degree of a Vertex - answer - in the graph is the number of edges of G incident with v except that a loop contributes twice to the degree of the vertex. Graphic - answer - A sequence of numbers is graphic if it is the degree sequence of a simple graph. Tournament - answer - directed graph where for each pair of vertices u and v either uv or vu an edge of T. one way to create a tournament is to start with a complete graph and assign a direction to each edge. Out degree - answer - The number of edges directed from v and is denoted by od v. the outrigger of a vertex is also the score of the vertex. Transmitter - answer - a vertex v with id v=0 and od v some number bigger than 0 Reciever - answer - a vertex with od v= 0 and id v some number bigger than 0. Digraph (Directed Graph) - answer - Graph in which each edge has a direction associated with it. Isomorphic - answer - if the vertices of the two graphs can be labeled with the numbers from 1 to n. Isomorphic: - answer - Must have same: -number of vertices -number of edges -degree sequence of the vertices Path - answer - list of vertices where each vertex in the list is adjacent to the previous and the next vertex circuit - answer - A path that never goes over the same edge more than once and returns to the starting vertex. Eulerian circuit - answer - circuit that uses each edge in a graph exactly once. (all vertices have even degrees) Eulerian trail - answer - if a graph has a path that is not a circuit that covers each edge exactly once Traversable Graph - answer - Graph that has eulerian trail Eulerian graph - answer - A graph is eulerian if it has a eulerian circuit Hamiltonian Circuit - answer - a route that passes through every vertex of G exactly once, and ends at the starting vertex Weight of a Path - answer - Sum of weights of the edges of the path. Traveling Salesman Problem - answer - What is the most efficient way to visit every vertex in a graph . Brute Force Method - answer - List all possible hamiltonian cycles and count weights. Nearest Neighbor Algorithm - answer - Connect the lines that have the smallest weights. Best edge algorithm - answer - choose best weights for each edges individually coloring - answer - assignment of a color to each vertex so that no two adjacent vertices share the same color Chromatic number - answer - minimum number of colors needed for a coloring of a graph. usually denoted with symbol X Four color theorem - answer - for any graph that may be drawn with no crossings edges x is at most 4.