diff options
Diffstat (limited to 'graf')
| -rw-r--r-- | graf/n1.lyx | 169 |
1 files changed, 98 insertions, 71 deletions
diff --git a/graf/n1.lyx b/graf/n1.lyx index 67c09b3..ea6dcba 100644 --- a/graf/n1.lyx +++ b/graf/n1.lyx @@ -204,32 +204,56 @@ finito \end_layout \begin_layout Standard -Dado un grafo +Dados un grafo \begin_inset Formula $G=(V,E)$ \end_inset -, si -\begin_inset Formula $v\in V$ + y +\begin_inset Formula $e:=(i,j)\in E$ \end_inset -, llamamos -\begin_inset Formula $G-v$ +, +\begin_inset Formula $i$ +\end_inset + + y +\begin_inset Formula $j$ \end_inset + son +\series bold +vértices extremos +\series default + de +\begin_inset Formula $e$ +\end_inset + +, +\begin_inset Formula $e$ +\end_inset + + es +\series bold +incidente +\series default a -\begin_inset Formula $(V\setminus\{v\},\{e\in E:v\notin e\})$ +\begin_inset Formula $i$ \end_inset -, y si -\begin_inset Formula $e\in E$ + y +\begin_inset Formula $j$ \end_inset -, llamamos -\begin_inset Formula $G-e$ + e +\begin_inset Formula $i$ \end_inset + es +\series bold +adyacente +\series default a -\begin_inset Formula $(V,E\setminus\{e\})$ +\begin_inset Formula $j$ \end_inset . @@ -241,7 +265,7 @@ Grafos y subgrafos \begin_layout Standard Un grafo -\begin_inset Formula $G:=(V,E)$ +\begin_inset Formula $G=(V,E)$ \end_inset es @@ -359,7 +383,11 @@ subgrafo generador \end_inset . - Llamamos + +\end_layout + +\begin_layout Standard +Llamamos \series bold subgrafo \series default @@ -396,7 +424,61 @@ independiente \end_inset . - Un + Dado un grafo +\begin_inset Formula $G=(V,E)$ +\end_inset + +, si +\begin_inset Formula $V'\subseteq V$ +\end_inset + +, llamamos +\begin_inset Formula $G-V'$ +\end_inset + + al subgrafo de +\begin_inset Formula $G$ +\end_inset + + inducido por +\begin_inset Formula $V\setminus V'$ +\end_inset + +, y si +\begin_inset Formula $E'\subseteq E$ +\end_inset + +, llamamos +\begin_inset Formula $G-E'$ +\end_inset + + a +\begin_inset Formula $(V,E\setminus E')$ +\end_inset + +. + Si +\begin_inset Formula $v\in V$ +\end_inset + +, +\begin_inset Formula $G-v:=G-\{v\}$ +\end_inset + +, y si +\begin_inset Formula $e\in E$ +\end_inset + +, +\begin_inset Formula $G-e:=G-\{e\}$ +\end_inset + +. + +\end_layout + +\begin_layout Standard +Un \series bold cliqué \series default @@ -417,6 +499,7 @@ maximal \end_inset . + \end_layout \begin_layout Standard @@ -451,62 +534,6 @@ isomorfismo de grafos . \end_layout -\begin_layout Standard -Dados un grafo -\begin_inset Formula $G=(V,E)$ -\end_inset - - y -\begin_inset Formula $e:=(i,j)\in E$ -\end_inset - -, -\begin_inset Formula $i$ -\end_inset - - y -\begin_inset Formula $j$ -\end_inset - - son -\series bold -vértices extremos -\series default - de -\begin_inset Formula $e$ -\end_inset - -, -\begin_inset Formula $e$ -\end_inset - - es -\series bold -incidente -\series default - a -\begin_inset Formula $i$ -\end_inset - - y -\begin_inset Formula $j$ -\end_inset - - e -\begin_inset Formula $i$ -\end_inset - - es -\series bold -adyacente -\series default - a -\begin_inset Formula $j$ -\end_inset - -. -\end_layout - \begin_layout Section Grado de un nodo \end_layout @@ -1070,7 +1097,7 @@ Sea \begin_inset Formula $d_{i}$ \end_inset -, luego +, luego \begin_inset Formula $\sum_{i=1}^{k}o(i)\leq2\binom{k}{2}+\sum_{i=k+1}^{n}\min\{k,d_{i}\}$ \end_inset |
