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Minimum supports of functions on the Hamming graphs with spectral constraints
- Source :
- Discrete Mathematics. 342:1351-1360
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- We study functions defined on the vertices of the Hamming graphs $H(n,q)$. The adjacency matrix of $H(n,q)$ has $n+1$ distinct eigenvalues $n(q-1)-q\cdot i$ with corresponding eigenspaces $U_{i}(n,q)$ for $0\leq i\leq n$. In this work, we consider the problem of finding the minimum possible support (the number of nonzeros) of functions belonging to a direct sum $U_i(n,q)\oplus U_{i+1}(n,q)\oplus\ldots\oplus U_j(n,q)$ for $0\leq i\leq j\leq n$. For the case $n\geq i+j$ and $q\geq 3$ we find the minimum cardinality of the support of such functions and obtain a characterization of functions with the minimum cardinality of the support. In the case $n \frac{n}{2}$,$\,q\ge 5$.<br />Comment: 17 pages, 3 figures
- Subjects :
- Discrete mathematics
Direct sum
020206 networking & telecommunications
0102 computer and information sciences
02 engineering and technology
Characterization (mathematics)
01 natural sciences
Theoretical Computer Science
Combinatorics
Hamming graph
010201 computation theory & mathematics
FOS: Mathematics
0202 electrical engineering, electronic engineering, information engineering
Mathematics - Combinatorics
Discrete Mathematics and Combinatorics
Cardinality (SQL statements)
Combinatorics (math.CO)
Adjacency matrix
05C50
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- ISSN :
- 0012365X
- Volume :
- 342
- Database :
- OpenAIRE
- Journal :
- Discrete Mathematics
- Accession number :
- edsair.doi.dedup.....42b9bc87ce3dbeea47c0d756d59afeb5