This preview shows page 1. Sign up to view the full content.
AMS 301.1 HOMEWORK # 1
Prof. Tucker
Spring, 2008
Section 1.1:
for 1,9,23 see answer in back of text;
6a) 5 vertices, b) 9 vertices;
14.,many possibilities, 16a)
(
a
,
b
), (
a
,
g
) and (
c
,
d
), (
d
,
e)
and (
c,d
), (
e
,
f)
and (
d
,
e
), (
e
,
f
),
b) {
b
,g
}
, {
b
,f
}
, {
c
,
f
}, {
c
,
e
}, {
d
,
f
},
c) 3 (the edges
incident to any vertex);
20.
.
•
•
•
•
O
O
O
O
•
•
•
•
O
O
O
•
•
•
•
O
Block surveillance vertices = •
Corner surveillance vertices =
a)
b)
•
•
•
•
O
O
O
c)
O
•
•
•
•
O
O
O
•
•
•
•
Section 1.2
:
5bck 7, see answer in back: 4. Not isomorphic
,
6c) no, complement of left graph is 2 4circuits,
d) no, 5degree and degree3 vertices form a triangle only in right graph,
e) No, only right graph has triangles;
Section 1.3
:
1, See answer in back of text: 4.
n
is odd and so parity of deg. is samein complement. Ans:
n
1
6. Make graph with vertex = team, edge = game. Within a given conference, the
subgraph consists of 13 vertices,
each of degree 11— contradicting Corollary
10b) (A,Z) (B,X)(C,Y)  (D,W)  (C,U)  (B,V)  (A,T)  (B,R)
(C,S)  (M,M) .
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/19/2010 for the course AMS 301 taught by Professor Arkin during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 ARKIN

Click to edit the document details