Mathematical Structures: History of Graphs

# History of Graphs

 Revision 2 . . July 22, 2004 3:28 pm by Jipsen Revision 1 . . July 8, 2004 1:54 pm by Jipsen

Difference (from prior major revision) (no other diffs)

Changed: 28,30c28,29
 \Large Name of class \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit} % Note: replace "Template" with Name_of_class in previous line

Changed: 32c31
 \abbreviation{Abbr}
 \abbreviation{Gph}

Changed: 35,36c34
 A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that
 A graph is a structure $\mathbf{G}=\langle G, E\rangle$ such that

Changed: 38c36
 $\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class}
 $G$ is a set,

Changed: 40c38
 $op_1$ is (name of property): $axiom_1$
 $E$ is a binary relation on $G$: $E\subseteq G\times G$, and

Changed: 42c40
 $op_2$ is ...: $...$
 $E$ is symmetric: $xEy\implies yEx$

Changed: 51,52c49,50
 Let $\mathbf{A}$ and $\mathbf{B}$ be ... . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x ... y)=h(x) ... h(y)$
 Let $\mathbf{G}$ and $\mathbf{H}$ be graphs. A morphism from $\mathbf{G}$ to $\mathbf{H}$ is a function $h:G\rightarrow H$ that is a homomorphism: $xE^{\mathbf G}y\implies h(x)\,E^{\mathbf H}\,h(y)$.