Hi! Can someone please help me with these DISCRETE MATH problems? It goes as fol
ID: 3770942 • Letter: H
Question
Hi! Can someone please help me with these DISCRETE MATH problems?
It goes as follows:
Use Graphs G1 and G2 to answer the following questions
a. Find the Adjancency Matrices of G! and G2 (justify)
b. Find the degree of vertices of G1 and G2 (justify)
c. Is G1 a Bipartite? Is G2 a Bipartite? (Justify your answers)
d. Are G1 and G2 ISOMORPHIC? (Show all the steps of your answer.)
e. Find the number of paths of length two between the vertices of Graph G2. (justify)
Any help will be greatly appreciated and rated ++++! Thanks!
Explanation / Answer
a. Find the Adjancency Matrices of G1 and G2
Graph G1:
a b c d e f g
a 0 1 1 0 0 1 1
b 1 0 1 1 0 0 1
c 1 1 0 1 1 0 0
d 0 1 1 0 1 1 0
e 0 0 1 1 0 1 1
f 1 0 0 1 1 0 1
g 1 1 0 0 1 1 0
Graph G2:
a' b' c' d' e' f' g'
a' 0 1 0 1 1 0 1
b' 1 0 1 0 1 1 0
c' 0 1 0 1 0 1 1
d' 1 0 1 0 1 0 1
e' 1 1 0 1 0 1 0
f' 0 1 1 0 1 0 1
g' 1 0 1 1 0 1 0
b. Find the degree of vertices of G1 and G2 (justify)
Graph G1:
Vertex Degree
a 4
b 4
c 4
d 4
e 4
f 4
g 4
Graph G2:
Vertex Degree
a' 4
b' 4
c' 4
d' 4
e' 4
f' 4
g' 4
d. G1 and G2 ISOMORPHIC
Number of vertices: both 7.
Number of edges: both 14.
Degrees of corresponding vertices: all degree 4.
Connectedness: Each is fully connected.
Number of connected components: Both 2.
Pairs of connected vertices: All correspond.
Number of loops: 0.
Number of parallel edges: 0.
Everything is equal and so the graphs G1 and G2 are isomorphic.
e. Find the number of paths of length two between the vertices of Graph G2.
total 7 paths of length 2
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