New upper bound for the cardinalities of s-distance sets on the unit sphere
نویسنده
چکیده
We have the Fisher type inequality and the linear programming bound as upper bounds for the cardinalities of s-distance sets on S d−1. In this paper, we give new upper bounds for the cardinalities of s-distance sets on S d−1 for any s. Those upper bounds is a generalization of the Fisher typer inequality and is useful for s-distance sets which are not applicable to the linear programming bound.
منابع مشابه
On a generalization of distance sets
A subset X in the d-dimensional Euclidean space is called a k-distance set if there are exactly k distinct distances between two distinct points in X and a subset X is called a locally k-distance set if for any point x in X , there are at most k distinct distances between x and other points in X . Delsarte, Goethals, and Seidel gave the Fisher type upper bound for the cardinalities of k-distanc...
متن کاملSome Edge Cut Sets and an Upper bound for Edge Tenacity of Organic Compounds CnH2n+2
The graphs play an important role in our daily life. For example, the urban transport network can be represented by a graph, as the intersections are the vertices and the streets are the edges of the graph. Suppose that some edges of the graph are removed, the question arises, how damaged the graph is. There are some criteria for measuring the vulnerability of graph; the...
متن کاملPositive definite functions in distance geometry
I. J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a nonnegative linear combination of Gegenbauer polynomials. This fact play a crucial role in Delsarte’s method for finding bounds for the density of sphere packings on spheres and Euclidean spaces. One of the most excited applications of Delsarte’s method is a solution of the kissing ...
متن کاملSharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs
In $1994,$ degree distance of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative ver...
متن کاملDifferent-Distance Sets in a Graph
A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...
متن کامل