# K_4-free graphs of order 5 with \Delta(G)=4, m>=6

## 1468 days ago by Buyan

n=5 k=3 L=list(graphs(n)) g2=graphs.CompleteGraph(k+1) W=[] for g in L: if g.subgraph_search_count(g2)==0 and g.degree_sequence()[0]==4: W.append(g) graphs_list.show_graphs(W)
for g in W: V=g.vertices() m=g.size() sum=0 G=[] G.append(g) for v in V: for u in V: if g.has_edge(v,u): sum=sum+(g.degree(v)-1)*(g.degree(u)-1) html('$RM_2(g)=%s$ and the bound $\dfrac{m}{9}(6m-5) = %s$' %(sum/2, latex(m/9*(6*m-5)+m)) )
 $RM_2(g)=0$ and the bound $\dfrac{m}{9}(6m-5) = \frac{112}{9}$ $RM_2(g)=7$ and the bound $\dfrac{m}{9}(6m-5) = \frac{170}{9}$ $RM_2(g)=16$ and the bound $\dfrac{m}{9}(6m-5) = \frac{80}{3}$ $RM_2(g)=27$ and the bound $\dfrac{m}{9}(6m-5) = \frac{322}{9}$ $RM_2(g)=26$ and the bound $\dfrac{m}{9}(6m-5) = \frac{322}{9}$ $RM_2(g)=40$ and the bound $\dfrac{m}{9}(6m-5) = \frac{416}{9}$ $RM_2(g)=14$ and the bound $\dfrac{m}{9}(6m-5) = \frac{80}{3}$  and the bound and the bound and the bound and the bound and the bound and the bound and the bound