Re: Peirce's 1870 “Logic Of Relatives ” • Comment 8.5

Re:
JA:http://inquiryintoinquiry.com/2014/02/20/peirces-1870-logic-of-relatives-%E2%80%A2-comment-8-5/
CG:http://web.archive.org/web/20140222153200/http://permalink.gmane.org/gmane.science.philosophy.peirce/11855
JBD:http://web.archive.org/web/20140224152510/http://permalink.gmane.org/gmane.science.philosophy.peirce/11885

Jeff, List,

The word “graph” has two main senses in contemporary mathematical usage.

We use one sense in referring to the graph of a function or the graph of a relation, namely, the 
sets of points that satisfy the functional equation or that belong to the relation, respectively. 
There be subtleties here, but since that is not the sense I'm using in the present context, I'll 
tiptoe quietly by for the moment, leaving just this link for the more curious and hardy inquirer:

☞ http://intersci.ss.uci.edu/wiki/index.php/Relation_theory

We use another sense in the field of Graph Theory.  Here is a classic definition, one that manages 
to define in passing much of the language that we need for describing graphs and their properties:

<quote>

A ‘graph’ G consists of a finite nonempty set V = V(G) of p ‘points’ together with a prescribed set 
X of q unordered pairs of distinct points of V.  Each pair x = {u, v} of points in X is a ‘line’ of 
G, and x is said to ‘join’ u and v.  We write x = uv and say that u and v are ‘adjacent 
points’(sometimes denoted ‘u adj v’);  point u and line x are ‘incident’ with each other, as are v 
and x.  If two distinct lines x and y are incident with a common point, then they are ‘adjacent 
lines’.  A graph with p points and q lines is called a ‘(p, q) graph’.  The (1, 0) graph is ‘trivial’.

</quote> Harary, ‘Graph Theory’, p. 9.

Select Bibliography
-------------------

Elementary Graph Theory:

| Frank Harary,
|‘Graph Theory’,
| Addison-Wesley, Reading, MA, 1969.

Enumerative Graph Theory:

| Frank Harary & Edgar M. Palmer,
|‘Graphical Enumeration’,
| Academic Press, New York, NY, 1973.

Asymptotic Graph Theory:

| Edgar M. Palmer,
|‘Graphical Evolution : An Introduction to the Theory of Random Graphs’,
| John Wiley & Sons, New York, NY, 1985.

Algorithmic Graph Theory:

| Shimon Even,
|‘Graph Algorithms’,
| Computer Science Press, Rockville, MD, 1979.

Have to break here ...
More later ...

Jon

-- 

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