منابع مشابه
Notes on simplicial rook graphs
The simplicial rook graph SR(m,n) is the graph of which the vertices are the sequences of nonnegative integers of length m summing to n, where two such sequences are adjacent when they differ in precisely two places. We show that SR(m,n) has integral eigenvalues, and smallest eigenvalue s = max(−n,− ( m 2 ) ), and that this graph has a large part of its spectrum in common with the Johnson graph...
متن کاملOn the Spectra of Simplicial Rook Graphs
The simplicial rook graph SR(d, n) is the graph whose vertices are the lattice points in the nth dilate of the standard simplex in R, with two vertices adjacent if they differ in exactly two coordinates. We prove that the adjacency and Laplacian matrices of SR(3, n) have integral spectra for every n. We conjecture that SR(d, n) is integral for all d and n, and give a geometric construction of a...
متن کاملSPECTRAL AND COMBINATORIAL PROPERTIES OF FRIENDSHIP GRAPHS, SIMPLICIAL ROOK GRAPHS, AND EXTREMAL EXPANDERS by
Algebraic combinatorics is the area of mathematics that uses the theories and methods of abstract and linear algebra to solve combinatorial problems, or conversely applies combinatorial techniques to solve problems in algebra. In particular, spectral graph theory applies the techniques of linear algebra to study graph theory. Spectral graph theory is the study of the eigenvalues of various matr...
متن کاملRook-drawings of Plane Graphs
We introduce a new type of graph drawing called “rook-drawing”. A rook-drawing of a graph G is obtained by placing the n nodes of G on the intersections of a regular grid, such that each row and column of the grid supports exactly one node. This paper focuses on rook-drawings of planar graphs. We first give a linear algorithm to compute a planar straight-line rook-drawing for outerplanar graphs...
متن کاملChannel Assignment on Strongly-Simplicial Graphs
Given a vector ( 1; 2; : : : ; t) of non increasing positive inte gers, and an undirected graph G = (V;E), an L( 1; 2; : : : ; t)-coloring of G is a function f from the vertex set V to a set of nonnegative inte gers such that jf(u) f(v)j i, if d(u; v) = i; 1 i t; where d(u; v) is the distance (i.e. the minimum number of edges) between the vertic es u and v. This paper presents e cient algorithm...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2015
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-015-0633-y