Determine if the graph is Hamiltonian graph I am supposed to determine if the following graph is a Hamiltonian graph:
$G=(V,E)$ where $V=\{1,2,...,13\}$ and the set of edges is defined as follow: $E=\{(i,j)\in V\times V|11\leq i + j \leq 15\}$.   
My Attempt:
I draw it and I found out, that it does not contain bridge or articulation.We learnt Dirac and Ore theorem, but none of this is applicable. So I have to find Hamiltonian circle, but I do not know how, because I think this is complicated graph for doing so. 
Can  anyone help me?

The graph is Hamiltonian, here are two Hamilton cycles:
$(7,8,5,10,3,12,1,13,2,11,4,9,6,7)$
$(7,8,5,10,3,12,2,13,1,11,4,9,6,7)$
I constructed this cycle starting from the vertex $13$ whose neighbors are only the vertex $1,2$.
