Let G = (V, E) be a connected planar multigraph. Consider a planar embedding of G with F faces. Recall that the degree of a face is the length of its facial walk. Show that if every face has degree 4, then |E = 2|V| – 4. %3!

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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please send handwritten solution for Q2 part b

(a) Apply the (i) depth-first search and
(ii) breadth-first search algorithms
to the following graph. Root your search
tree at 1 and use the natural ordering on
the vertices.
10
(b) Let G = (V, E) be a connected planar multigraph. Consider a planar embedding of G with F faces.
Recall that the degree of a face is the length of its facial walk. Show that if every face has degree 4,
then |E = 2|V| – 4.
%3D
Transcribed Image Text:(a) Apply the (i) depth-first search and (ii) breadth-first search algorithms to the following graph. Root your search tree at 1 and use the natural ordering on the vertices. 10 (b) Let G = (V, E) be a connected planar multigraph. Consider a planar embedding of G with F faces. Recall that the degree of a face is the length of its facial walk. Show that if every face has degree 4, then |E = 2|V| – 4. %3D
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