Math 110 Exam 3 Study Guide with
Complete Solutions
Adjacent Edges - ANSWER-2 edges with a common vertex
Adjacent Vertices - ANSWER-2 vertices connected by one edge
Area of a circle - ANSWER-A=πr²
Circuit or Cycle - ANSWER-A trail that begins and ends at the same vertex
Circumference - ANSWER-C=2πr
Cone - ANSWER-V=1/3πr^2h
Cylinder - ANSWER-V=πr²h
SA=2πrh + 2πr²
Degree of a Node - ANSWER-- number of edges incident with that node
- by incident we mean "touching"
Diameter - ANSWER-d=2r
Edges - ANSWER-Lines connecting the points
Euler Circuit - ANSWER-- A ____________ that travels through every edge exactly
once
- Returns to starting point
Euler Circuit - ANSWER-A connected graph with ONLY EVEN vertices
Euler Trail - ANSWER-- A _________ that travels through every edge exactly once
- Does not return to starting point
Euler Trail - ANSWER-A connected graph with EXACTLY TWO ODD degree vertices
Euler's Theorems - ANSWER-1. A connected graph with ONLY EVEN degree vertices
has an EULER CIRCUIT
2. A connected graph with EXACTLY TWO ODD degree vertices has an EULER TRAIL
3. A connected graph with MORE THAN TWO ODD-degree vertices has neither
4. A disconnected graph has NEITHER
Graph - ANSWER-- made up of vertices or nodes
- edges the lines connecting the vertices
Complete Solutions
Adjacent Edges - ANSWER-2 edges with a common vertex
Adjacent Vertices - ANSWER-2 vertices connected by one edge
Area of a circle - ANSWER-A=πr²
Circuit or Cycle - ANSWER-A trail that begins and ends at the same vertex
Circumference - ANSWER-C=2πr
Cone - ANSWER-V=1/3πr^2h
Cylinder - ANSWER-V=πr²h
SA=2πrh + 2πr²
Degree of a Node - ANSWER-- number of edges incident with that node
- by incident we mean "touching"
Diameter - ANSWER-d=2r
Edges - ANSWER-Lines connecting the points
Euler Circuit - ANSWER-- A ____________ that travels through every edge exactly
once
- Returns to starting point
Euler Circuit - ANSWER-A connected graph with ONLY EVEN vertices
Euler Trail - ANSWER-- A _________ that travels through every edge exactly once
- Does not return to starting point
Euler Trail - ANSWER-A connected graph with EXACTLY TWO ODD degree vertices
Euler's Theorems - ANSWER-1. A connected graph with ONLY EVEN degree vertices
has an EULER CIRCUIT
2. A connected graph with EXACTLY TWO ODD degree vertices has an EULER TRAIL
3. A connected graph with MORE THAN TWO ODD-degree vertices has neither
4. A disconnected graph has NEITHER
Graph - ANSWER-- made up of vertices or nodes
- edges the lines connecting the vertices
