12. Graph and Their Applications

12. Graph and Their Applications - Graph and Its...

• Notes
• 11

This preview shows pages 1–5. Sign up to view the full content.

Graph and Its Applications 1

This preview has intentionally blurred sections. Sign up to view the full version.

Graph Nonlinear data Structures. A graph G consists of two properties: (a) A set V of elements called vertices or nodes. (b) A set E of connectors called edges such that each edge e is identified as e = [u,v] (unordered pair of vertices). Here u and v are called endpoints of e and they are said to be the adjacent nodes or neighbors . Example: A B C D E In Graph G 1 5 Vertices:{A, B, C, D, E} 6 Edges: {[A,B], [A,C], [B,D], [B,E], [C,D], [D,E]} Figure1: A graph G 1 Graph and Their Applications Graph and Their Applications 2
Definitions Isolated Node: A vertex u with no edges. Path: A path P of length n from a node u to node v is defined as a sequence n+1 nodes such that P=(v 0 , v 1 , ….v n ). (a) Simple Path: if all nodes in path P are distinct. (b) Closed Path: If node v 0 = v n . Cycle: A closed path, with no other repeated vertices other than the starting and the ending vertices. Example: A B C D E In graph G 2 Isolate Node: E Path P: A, B, D, C • Cycle C 1 : A, B, D, C, A Figure2: Graph G 2 3

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Winter '10
• Leong
• Graph Theory, Sequential Representation

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern