# Difference between revisions of "Talk:Graph"

Knkillname (talk | contribs) (Created page with "== Notation == The graph notation is not fixed thorough this article. * First we are presented with the notation $G\left(V,E\right)$, which uses the symbol $G$ as a functor to...") |
Knkillname (talk | contribs) |
||

Line 5: | Line 5: | ||

* Finally $G_1=G(V_1,E_1)$ and $G_2=G(V_2,E_2)$ again uses $G$ as a functor. | * Finally $G_1=G(V_1,E_1)$ and $G_2=G(V_2,E_2)$ again uses $G$ as a functor. | ||

Even Boundy & Murty (Graph Theory, Graduate Texts in Mathematics, Springer) which notation has become kind of standard, have some difficulty defining what a graph is from a set theoretical standpoint. They say "a <i>graph</i> $G$ is an ordered pair $\left(V(G), E(G)\right)$ consisting of a set $V(G)$ of <i>vertices</i> and a set $E(G)$, disjoint form $V(G)$, of <i>edges</i>, together with an <i>incidence function</i> $\psi_G$ that associates with each edge of $G$, an unordered pair of (not necessarily distinct) vertices of $G$". So that it is an ordered pair with an extra thing outside of that ordered pair. | Even Boundy & Murty (Graph Theory, Graduate Texts in Mathematics, Springer) which notation has become kind of standard, have some difficulty defining what a graph is from a set theoretical standpoint. They say "a <i>graph</i> $G$ is an ordered pair $\left(V(G), E(G)\right)$ consisting of a set $V(G)$ of <i>vertices</i> and a set $E(G)$, disjoint form $V(G)$, of <i>edges</i>, together with an <i>incidence function</i> $\psi_G$ that associates with each edge of $G$, an unordered pair of (not necessarily distinct) vertices of $G$". So that it is an ordered pair with an extra thing outside of that ordered pair. | ||

+ | Even so, we should fix a notation. | ||

--[[User:Knkillname|M. Abarca]] ([[User talk:Knkillname|talk]]) 19:37, 21 August 2014 (CEST) | --[[User:Knkillname|M. Abarca]] ([[User talk:Knkillname|talk]]) 19:37, 21 August 2014 (CEST) |

## Revision as of 17:38, 21 August 2014

## Notation

The graph notation is not fixed thorough this article.

- First we are presented with the notation $G\left(V,E\right)$, which uses the symbol $G$ as a functor to create a graph from two sets $V$ and $E$. As a programmer, this notation is nice because it is akin of how object-oriented programming works.
- Then $H\left(W,I\right)$ implies that $G$ is not a functor at all, but the notation $G(V,E)$ is a mere abbreviation for $G=(V,E)$.
- Finally $G_1=G(V_1,E_1)$ and $G_2=G(V_2,E_2)$ again uses $G$ as a functor.

Even Boundy & Murty (Graph Theory, Graduate Texts in Mathematics, Springer) which notation has become kind of standard, have some difficulty defining what a graph is from a set theoretical standpoint. They say "a *graph* $G$ is an ordered pair $\left(V(G), E(G)\right)$ consisting of a set $V(G)$ of *vertices* and a set $E(G)$, disjoint form $V(G)$, of *edges*, together with an *incidence function* $\psi_G$ that associates with each edge of $G$, an unordered pair of (not necessarily distinct) vertices of $G$". So that it is an ordered pair with an extra thing outside of that ordered pair.
Even so, we should fix a notation.
--M. Abarca (talk) 19:37, 21 August 2014 (CEST)

**How to Cite This Entry:**

Graph.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Graph&oldid=33050