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pro vyhledávání: '"Russell Merris"'
Autor:
Russell Merris
Publikováno v:
The American Mathematical Monthly. 125:764-768
Autor:
Russell Merris
Publikováno v:
Linear and Multilinear Algebra. 65:1927-1933
Pioneering multilinear algebraist Marvin Marcus died 20 February 2016.Marvin Marcus with 1.5-year-old son Jeffrey in 1956. Source: Photo courtesy of Marvin’s daughter, Karen Melissa MarcusAfter obt...
Autor:
Robert Grone, Russell Merris
Publikováno v:
Linear Algebra and its Applications. 428(7):1565-1570
A graph that can be constructed from isolated vertices by the operations of union and complement is decomposable. Every decomposable graph is Laplacian integral. i.e., its Laplacian spectrum consists entirely of integers. An indecomposable graph is n
Autor:
Russell Merris
Publikováno v:
Linear and Multilinear Algebra. 45:275-285
If G is a graph on n vertices, its Laplacian matrix L(G) = D(G) - A(G) is the difference of the diagonal matrix of vertex degrees and the adjacency matrix. The main purpose of this note is to conti...
Autor:
Russell Merris
Publikováno v:
Linear Algebra and its Applications. 278:221-236
If G is a graph, its Laplacian is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. The main thrust of the present article is to prove several Laplacian eigenvector “principles” which in certain cases can be us
Publikováno v:
Journal of Chemical Information and Computer Sciences. 38:62-65
A relation has been recently established between the Wiener number W and an immanant of the Laplacian matrix of the molecular graph [Chan, O.; Lam, T. K.; Merris, R. J. Chem. Inf. Comput. Sci. 1997, 37, 762−765]. On the basis of this result we now
Publikováno v:
Journal of Chemical Information and Computer Sciences. 37:762-765
In this work, we show that the Wiener number of an acyclic molecule may be expressed as a linear function of a hook immanant of the Laplacian matrix associated with the molecule. This relation leads to a new interpretation of the Wiener number as a w
Autor:
Russell Merris
Publikováno v:
Linear and Multilinear Algebra. 43:201-205
Two graphs are isomorphic only if they are Laplacian isospectral, that is, their Laplacian matrices share the same multiset of eigenvalues. Large families of nonisomorphic Laplacian isospectral gra...
Autor:
Russell Merris
Publikováno v:
Linear and Multilinear Algebra. 39:19-31
Let G be a graph on n vertices. Its Laplacian is the n-by-n matrix L(G)−D(G)−A(G), where D(G) is the diagonal matrix of vertex degrees and A(G) is the (0,1)-adjacency matrix of G. This article surveys recent results on graph Laplacians.
Autor:
Russell Merris
Publikováno v:
Publikacije Elektrotehnickog fakulteta - serija: matematika. :1-3
A graph on n vertices is antiregular if its vertex degrees take on n ? 1 different values. For every n ? 2 there is a unique connected antiregular graph on n vertices. Call it An. (The unique disconnected antiregular graph on n vertices is Acn.) The