My Publications
Lists of Conjectures
On Graph Listings & Graph Invariants
 For collections of graphs see B. McKay's
combinatorial data page.
 For
a listing and drawings of small graphs and Java applet for
investigating classes of graphs see
ISCGI
project.
 For some tables of graphs, computed graph invariants and
conjectures see
S. Speed's
page.
 For some tables of distributions of computed graph invariants
(chromatic number & chromatic index) see
K Briggs
page.
 While working on improving the performance of some of
my code for various dominating sets, I found the following
distributions interesting.
The following are frequencies of values for
all
connected 9vertex graphs, where g
is the domination number,
g_{t}
is the total domination
number, i is the independent domination number,
g_{2}
is the 2domination
number (doubledomination), a
is the independence
number, a_{crit}
is the critical independence
number and a_{core
}the order of the
intersection of all maximum independent sets. 
value 
# with
g=value 
# with
g_{t}=value 
# with
i=value 
# with
g_{2}=value 
# with
a=value 
# with
a_{crit}=value 
# with
a_{core}=value 
0 
0 
0 
0 
0 
0 
184593 
84231 
1 
12346 
0 
12346 
0 
1 
33235 
32914 
2 
219823 
183149 
198678 
2054 
1892 
11913 
33683 
3 
28720 
70667 
49086 
102428 
100702 
8529 
39855 
4 
191 
7151 
969 
132775 
135563 
254 
54593 
5 

111 
1 
22007 
21782 
21419 
14835 
6 

2 

1729 
1105 
1102 
936 
7 



84 
34 
34 
32 
8 



3 
1 
1 
1 
9 







Graffiti History and My Collaboration on
Graffiti
 Graffiti is a computer program that makes conjectures in mathematics
and chemistry. Around 1985,
Siemion Fajtlowicz developed the first
version of Graffiti, which generated conjectures of interest to many
well known researchers. A list of conjectures of Graffiti,
Written on the Wall, maintained by Fajtlowicz. I update a growing
bibliography
of many papers inspired by Graffiti (which also includes some that
simply mention or compare Graffiti.)
 My collaboration with Fajtlowicz on Graffiti began around 1990 (as
his student), at this time we began developing the newest versions of
Graffiti, called Forever, Whatever and Dalmatians. Some descriptions of
these versions are available in my paper On Some History of the Development of Graffiti (2003) and also in papers by Fajtlowicz
and Larson.
 In addition to coauthoring the new versions and resolving many
conjectures, I have resumed extending the list of conjectures
Written on the Wall II generated by Graffiti (conjectures 18) and now also Graffiti.pc
(conjectures 9 and on.)
Educational Applications of Graffiti (and Graffiti.pc)
 In the Spring of 2001, as an educational experiment, my
undergraduate student Barbara Chervenka explored graph theory through
conjectures of Graffiti. She maintained a chronology of conjectures and
their resolutions, and presented a
poster
at Combinatexas 2001). On the similar topic she gave a Pi Mu Epsilon
student presentation titled "Exploring Graph Theory Through Conjectures
of Graffiti" at MathFest 2001, and at DIMACS in 2001 discussing her use
of Graffiti.pc. In the Summer
of 2001, another of my undergraduate students Kelly Wroblewski conducted
a similar project utilizing Graffiti.pc and presented the results of the project in the
poster
session of the CST Student Research Conference in November 2001. There
is a page with these and all
subsequent
Graffiti.pc undergraduate projects.
 In the spring of 2002, Gunnar Brinkmann at the University of Bielefeld (Germany) also used Graffiti.pc
for a graduate mathematics education course.. Further, in the spring of 2004
he conducted a workshop for advanced high school teachers.
 For similar applications, see
Fajtlowicz's
webpage
and Ryan Pepper's paper "On New Didactics of Mathematics: Learning Graph Theory
via Graffiti"..
Graffiti.pc
 In the summer of 2001, I developed a pcplatform program called
Graffiti.pc. For a description of my program and of the above mentioned educational applications see my paper,
Graffiti.pc:
A Variant of Graffiti (2002)
(pdf).
Pictures
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