Number and Algebra
Functions
Geometry and Trigonometry
Statistics and Probability
Calculus
Given the simple graph GGG with vertex set V=A,B,C,DV = \\{A, B, C, D\\}V=A,B,C,D and edge set E=A,B,A,C,B,C,C,DE = \\{\\{A,B\\},\\{A,C\\},\\{B,C\\},\\{C,D\\}\\}E=A,B,A,C,B,C,C,D, determine the degree of each vertex and list the vertices adjacent to CCC.
In a simple undirected graph GGG with 6 vertices and 9 edges, calculate the sum of degrees of all vertices and confirm the Handshaking Lemma.
Decide whether the simple graph with vertices {V1,V2,V3,V4,V5}\{V_1,V_2,V_3,V_4,V_5\}{V1,V2,V3,V4,V5} and edges V1,V2,V2,V3,V3,V4,V4,V5,V5,V1\\{V_1,V_2\\},\\{V_2,V_3\\},\\{V_3,V_4\\},\\{V_4,V_5\\},\\{V_5,V_1\\}V1,V2,V2,V3,V3,V4,V4,V5,V5,V1 is complete, connected, and contains any circuits. Justify your answers.
Given the adjacency matrix
list the adjacency list representation of the corresponding graph.
Given a simple graph GGG with vertices 111 to 666 and edge set 1,2,2,3,3,1,4,5,5,6,6,4}\\{1,2\\},\\{2,3\\},\\{3,1\\},\\{4,5\\},\\{5,6\\},\\{6,4\\}\}1,2,2,3,3,1,4,5,5,6,6,4}. Is GGG connected? Find all connected components and determine if GGG contains any circuits.
Consider the electrical circuit where nodes 1,2,3,41,2,3,41,2,3,4 are junctions and resistors connect nodes (1,2),(2,3),(3,4),(4,1)(1,2),(2,3),(3,4),(4,1)(1,2),(2,3),(3,4),(4,1) and (2,4)(2,4)(2,4). Represent this circuit as a simple graph and find the degree of each vertex.
A simple graph GGG has adjacency matrix
Given friendship strengths between five people A,B,C,D,EA,B,C,D,EA,B,C,D,E as follows:
If a friendship strength ≥6\ge6≥6 defines an edge, draw the corresponding simple graph and list the degree of each vertex.
Given the simple graph GGG defined by adjacency list: 1: {2,3}, 2: {1,3,4}, 3: {1,2,4}, 4: {2,3,5}, 5: {4}. Determine whether GGG contains an Eulerian trail or circuit.
Construct a simple graph with 7 vertices labeled P,Q,R,S,T,U,VP,Q,R,S,T,U,VP,Q,R,S,T,U,V such that deg(P)=3(P)=3(P)=3, deg(Q)=3(Q)=3(Q)=3, deg(R)=2(R)=2(R)=2, deg(S)=2(S)=2(S)=2, deg(T)=2(T)=2(T)=2, deg(U)=1(U)=1(U)=1, deg(V)=1(V)=1(V)=1. Provide the edge set.
Given the degree sequence (3,3,2,2,2,2)(3,3,2,2,2,2)(3,3,2,2,2,2), determine whether there is a simple graph with this degree sequence and, if so, construct one.
Given degree sequence (4,3,3,2,2,1)(4,3,3,2,2,1)(4,3,3,2,2,1), determine if it is graphical, and if so, use the Havel–Hakimi algorithm to construct the corresponding simple graph.
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Question Type 2: Creating simple graphs given information of structures