Zobrazeno 1 - 10
of 164
pro vyhledávání: '"ABIAD, AIDA"'
Autor:
Abiad, Aida, Zhou, Jiang
For a graph $G$, its $k$-th power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$ of each other. The $k$-independence number $\alpha_k(G)$ is defined as the independence number of $G^k$. By using general s
Externí odkaz:
http://arxiv.org/abs/2411.09450
Autor:
Abiad, Aida, Peters, Louka
Local operations of combinatorial structures (graphs, Hadamard matrices, codes, designs) that maintain the basic parameters unaltered, have been widely used in the literature under the name of switching. We show an equivalence between two switching m
Externí odkaz:
http://arxiv.org/abs/2410.10638
A switching method is a graph operation that results in cospectral graphs (graphs with the same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most cospectral graphs with cospectral complements can be constructed using regul
Externí odkaz:
http://arxiv.org/abs/2410.07948
Hoffman's bound is a well-known spectral bound on the chromatic number of a graph, known to be tight for instance for bipartite graphs. While Hoffman colorings (colorings attaining the bound) were studied before for regular graphs, for irregular grap
Externí odkaz:
http://arxiv.org/abs/2407.02544
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all previously known bo
Externí odkaz:
http://arxiv.org/abs/2406.15926
In this note we apply a spectral method to the graph of alternating bilinear forms. In this way, we obtain upper bounds on the size of an alternating rank-metric code for given values of the minimum rank distance. We computationally compare our resul
Externí odkaz:
http://arxiv.org/abs/2405.09254
We derive eigenvalue bounds for the $t$-distance chromatic number of a graph, which is a generalization of the classical chromatic number. We apply such bounds to hypercube graphs, providing alternative spectral proofs for results by Ngo, Du and Grah
Externí odkaz:
http://arxiv.org/abs/2404.14839
In this note, we use eigenvalue interlacing to derive an inequality between the maximum degree of a graph and its maximum and minimum adjacency eigenvalues. The case of equality is fully characterized.
Externí odkaz:
http://arxiv.org/abs/2402.12915
The exact distance $t$-power of a graph $G$, $G^{[\sharp t]}$, is a graph which has the same vertex set as $G$, with two vertices adjacent in $G^{[\sharp t]}$ if and only if they are at distance exactly $t$ in the original graph $G$. We study the cli
Externí odkaz:
http://arxiv.org/abs/2402.00189
Autor:
Abiad, Aida, Zeijlemaker, Sjanne
A unified framework for the Expander Mixing Lemma for irregular graphs using adjacency eigenvalues is presented, as well as two new versions of it. While the existing Expander Mixing Lemmas for irregular graphs make use of the notion of volume (the s
Externí odkaz:
http://arxiv.org/abs/2401.07125