41. In the case of undirected graphs , this works because L is symmetric, and by the spectral theorem, its eigenvectors are all orthogonal. 42. Let \ lambda _ G ( v ) be the number of triangles on v \ in V ( G ) for undirected graph G. 43. The same problem for undirected graphs is called " undirected s-t connectivity " and was shown to be P-complete. 44. One may also consider playing either Geography game on an undirected graph ( that is, the edges can be traversed in both directions ). 45. More generally this result implies that every-edge-connected undirected graph can be oriented to form a-edge-connected directed graph. 46. In the " symmetric TSP ", the distance between two cities is the same in each opposite direction, forming an undirected graph . 47. Moreover, every undirected graph has an acyclic orientation, an assignment of a direction for its edges that makes it into a directed acyclic graph. 48. An undirected graph can be seen as a simplicial complex consisting of 1-simplices ( the edges ) and 0-simplices ( the vertices ). 49. Though, it may be possible to consider CTQW for directed graphs, we focus on this area as it applies to undirected graphs unless stated otherwise. 50. :So, for a given undirected graph , you want to know the number of talk ) 09 : 23, 24 September 2008 ( UTC)
