lec-7.pdf

# lec-7.pdf - Today Types of graphs Today Types of graphs...

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Today. Types of graphs.

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Today. Types of graphs. Complete Graphs. Trees. Hypercubes.
Today. Types of graphs. Complete Graphs. Trees. Hypercubes.

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Complete Graph. K n complete graph on n vertices.
Complete Graph. K n complete graph on n vertices. All edges are present.

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Complete Graph. K n complete graph on n vertices. All edges are present. Everyone is my neighbor.
Complete Graph. K n complete graph on n vertices. All edges are present. Everyone is my neighbor. Each vertex is adjacent to every other vertex.

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Complete Graph. K n complete graph on n vertices. All edges are present. Everyone is my neighbor. Each vertex is adjacent to every other vertex.
Complete Graph. K n complete graph on n vertices. All edges are present. Everyone is my neighbor. Each vertex is adjacent to every other vertex. How many edges?

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Complete Graph. K n complete graph on n vertices. All edges are present. Everyone is my neighbor. Each vertex is adjacent to every other vertex. How many edges? Each vertex is incident to n - 1 edges.
Complete Graph. K n complete graph on n vertices. All edges are present. Everyone is my neighbor. Each vertex is adjacent to every other vertex. How many edges? Each vertex is incident to n - 1 edges. Sum of degrees is n ( n - 1 ) .

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Complete Graph. K n complete graph on n vertices. All edges are present. Everyone is my neighbor. Each vertex is adjacent to every other vertex. How many edges? Each vertex is incident to n - 1 edges. Sum of degrees is n ( n - 1 ) . = Number of edges is n ( n - 1 ) / 2.
Complete Graph. K n complete graph on n vertices. All edges are present. Everyone is my neighbor. Each vertex is adjacent to every other vertex. How many edges? Each vertex is incident to n - 1 edges. Sum of degrees is n ( n - 1 ) . = Number of edges is n ( n - 1 ) / 2. Remember sum of degree is 2 | E | .

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K 4 and K 5 K 5 is not planar.
K 4 and K 5 K 5 is not planar. Cannot be drawn in the plane without an edge crossing!

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K 4 and K 5 K 5 is not planar. Cannot be drawn in the plane without an edge crossing! Prove it!
K 4 and K 5 K 5 is not planar. Cannot be drawn in the plane without an edge crossing! Prove it! Read Note 5!!

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Trees! Graph G = ( V , E ) . Binary Tree! More generally.
Trees: Definitions Definitions:

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Trees: Definitions Definitions: A connected graph without a cycle.
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