Doubly stochastic graph matrices Export

@article{citeulike:2371907, author = {Merris}, citeulike-article-id = {2371907}, comment = {cites "All Minors" paper * Laplacian is pos-definite by Gersgorin theorem * second smallest eigenvalue is >0 iff graph is connected * p.66(3) all-minors matrix-tree as interpretation of adjoint (Minors[mm[[2 ;;, 2 ;;]]] Array[(-1)^(\#1 + \#2) \&, {5, 5}]), ((j,k) entry of adjoint of H\_i is number of spanning trees with r,s in one tree, i in another). If r=s and r<->i is an edge, that gives number of spanning trees containing r<->i edge * Inverse(I+L(H)) is doubly stochastic iff H is connected}, journal = {Publ. Elektrotech. Fak. Univ. Beograd}, keywords = {doubly-stochastic, graph-theory}, posted-at = {2008-02-14 01:18:17}, priority = {2}, title = {Doubly stochastic graph matrices}, year = {1997} }

TY - JOUR ID - citeulike:2371907 L3 - citeulike-article-id:2371907 JF - Publ. Elektrotech. Fak. Univ. Beograd TI - Doubly stochastic graph matrices KW - doubly-stochastic KW - graph-theory N1 - cites "All Minors" paper * Laplacian is pos-definite by Gersgorin theorem * second smallest eigenvalue is >0 iff graph is connected * p.66(3) all-minors matrix-tree as interpretation of adjoint (Minors[mm[[2 ;;, 2 ;;]]] Array[(-1)^(#1 + #2) &, {5, 5}]), ((j,k) entry of adjoint of H_i is number of spanning trees with r,s in one tree, i in another). If r=s and r<->i is an edge, that gives number of spanning trees containing r<->i edge * Inverse(I+L(H)) is doubly stochastic iff H is connected AU - Merris PY - 1997/// ER -