Sec.	Pg.
Acknowledgements	0.1	iv
Updates and Correspondence	0.2	v
Notation and references	0.3	v
Layout of the thesis	0.5	vii
What was left out, and what wasn't	0.7	ix
A word of warning	0.12	xi
Nair's constructions	0.13	xi
1 Introduction and Fundamental Properties		1
Distance and connectivity	1.4	3
Degree sequences and antimorphisms	1.21	11
New graphs from old	1.26	13
Auto- and anti-morphisms	1.29	16
The structure of sc-graphs	1.36	21
Planarity and thickness	1.46	27
Eigenvalues	1.48	28
Chromaticity	1.57	32
The Hadwiger and Strong Perfect Graph Conjectures	1.64	36
The chromatic and total chromatic index	1.67	38
More Nordhaus-Gaddum results	1.74	41
2. Circuits, Paths and Cliques		45
Triangle numbers and paths	2.3	46
Circuits and Hamiltonicity	2.11	50
Circuits and Hamiltonicity in sc-tournaments	2.28	58
Ramsey Numbers	2.31	59
3. Regular Self-Complementary Graphs		63
Two interlocking hierarchies	3.3	64
Paley digraphs and generalisations	3.18	75
Characterisation of some vertex-transitive sc-digraphs	3.29	80
Strongly regular sc-graphs	3.32	81
Kotzig's problems	3.37	84
Antimorphisms with unequal cycle lengths	3.41	90
Open Problems	3.44	93
4. Self-Complementarity		97
The isomorphism problem	4.2	97
Generating self-complementary graphs	4.11	104
Self-complement indexes	4.19	111
Logical connections	4.32	117
The reconstruction conjectures	4.34	120
Codes and information	4.43	127
5. Generalisations of Self-Complementary Graphs		131
Self-complementary and self-converse digraphs	5.2	131
Multipartite self-complementary graphs	5.12	141
r-partite antimorphisms	5.15	142
Bipartite self-complementary graphs	5.20	145
Paths in r-partite sc-graphs	5.24	148
Diameters in r-psc-graphs	5.27	149
Almost self-complementary graphs	5.34	152
Isomorphic decompostitions	5.44	159
Cyclically t-complementary graphs	5.50	163
``Super-symmetrical'' graphs	5.59	167
6. Degree Sequences		171
Self-complementary graphs and digraphs	6.2	172
Edge degree sequences	6.9	175
Bipartite sc-graphs and bipartite sc-tournaments	6.17	179
Open problems	6.23	183
7. Enumeration		185
Definitions	7.2	186
Self-complementary graphs and digraphs	7.7	188
Prime order vertex-transitive digraphs	7.19	194
Relations and self-converse digraphs	7.27	200
Special types of graphs and digraphs	7.33	203
Colour cyclic factorisations	7.43	208
Self-complementary k-plexes	7.56	213
Self-complementary orbits and functions	7.59	215
Open problems	7.65	218
Bibliography		221--257