Page 1 Graph Theory: Lecture No. 16 Graph Theory: Lecture No. 16 L. Sunil Chandran Computer Science and Automation, Indian Institute of Science, Bangalore Email: sunil@csa.iisc.ernet.in Page 2 Graph Theory: Lecture No. 16 Graph Theory: Lecture No. 16 L. Sunil Chandran Computer Science and Automation, Indian Institute of Science, Bangalore Email: sunil@csa.iisc.ernet.in Graph Theory: Lecture No. 16 Let G be a graph with maximum degree ¢. Then ¢·Â 0 (G)· ¢+1. Page 3 Graph Theory: Lecture No. 16 Graph Theory: Lecture No. 16 L. Sunil Chandran Computer Science and Automation, Indian Institute of Science, Bangalore Email: sunil@csa.iisc.ernet.in Graph Theory: Lecture No. 16 Let G be a graph with maximum degree ¢. Then ¢·Â 0 (G)· ¢+1. Graph Theory: Lecture No. 16 A graph drawn on the plane in such way that no two edges intersect other than at the end points is called a plane graph. Abstract graphs that can be drawn in this way are called planar. Page 4 Graph Theory: Lecture No. 16 Graph Theory: Lecture No. 16 L. Sunil Chandran Computer Science and Automation, Indian Institute of Science, Bangalore Email: sunil@csa.iisc.ernet.in Graph Theory: Lecture No. 16 Let G be a graph with maximum degree ¢. Then ¢·Â 0 (G)· ¢+1. Graph Theory: Lecture No. 16 A graph drawn on the plane in such way that no two edges intersect other than at the end points is called a plane graph. Abstract graphs that can be drawn in this way are called planar. Graph Theory: Lecture No. 16 Euler's Formula: Let G be a connected plane graph with n vertices, m edges and ` faces. Then n¡m+` = 2. Page 5 Graph Theory: Lecture No. 16 Graph Theory: Lecture No. 16 L. Sunil Chandran Computer Science and Automation, Indian Institute of Science, Bangalore Email: sunil@csa.iisc.ernet.in Graph Theory: Lecture No. 16 Let G be a graph with maximum degree ¢. Then ¢·Â 0 (G)· ¢+1. Graph Theory: Lecture No. 16 A graph drawn on the plane in such way that no two edges intersect other than at the end points is called a plane graph. Abstract graphs that can be drawn in this way are called planar. Graph Theory: Lecture No. 16 Euler's Formula: Let G be a connected plane graph with n vertices, m edges and ` faces. Then n¡m+` = 2. Graph Theory: Lecture No. 16 A plane graph with n¸ 3 vertices has at most 3n¡6 edges.Read More
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