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Some results on Hamming graphs and an extended Hamming graphs
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Zafari, Ali, Alikhani, Saeid
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Isometric embeddings in Hamming graphs
Journal of Combinatorial Theory, Series B, 1990 An \(O(n^ 3)\)-algorithm is established which embeds a given graph isometrically into a Hamming graph (i.e., a Cartesian product of complete graphs) whenever possible, and recognizes non-embeddable graphs. From the algorithm several characterizations of the embeddable graphs are derived.
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On a Conjecture Regarding Identification in Hamming Graphs
The Electronic Journal of Combinatorics, 2019 In 2013, Goddard and Wash studied identifying codes in the Hamming graphs $K_q^n$. They stated, for instance, that $\gamma^{ID}(K_q^n)\leqslant q^{n-1}$ for any $q$ and $n\geqslant 3$. Moreover, they conjectured that $\gamma^{ID}(K_q^3)=q^2$. In this article, we show that $\gamma^{ID}(K_q^3)\leqslant q^2-q/4$ when $q$ is a power of four, which ...
Ville Junnila +2 more
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Graphs and CombinatoricsThe Hamming graph $H(n,q)$ is defined on the vertex set $[q]^n$ and two vertices are adjacent if and only if they differ in precisely one coordinate. Alon \cite{Alon} proved that the burning number of $H(n,2)$ is $\lceil\frac n2\rceil+1$. In this note we give a short proof of a fact that the burning number of $H(n,q)$ is $(1-\frac 1q)n+O(\sqrt{n\log n})
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On an isoperimetric problem for Hamming graphs
Discrete Applied Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Completely Transitive Codes in Hamming Graphs
European Journal of Combinatorics, 1999 A code \(C\) in the graph \(\Gamma\) is a non-empty subset of the vertex set \(V\) of \(\Gamma\). Completely transitive codes are a special class of completely regular codes. A code in the graph \(\Gamma\) is called a completely transitive code if there exists a subgroup \(G\) of the group of automorphisms of \(\Gamma\), such that each cell \(C_i\) in ...
Michael Giudici, Cheryl E. Praeger
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Randomized Communication and Implicit Graph Representations [PDF]
TheoretiCSWe initiate the focused study of constant-cost randomized communication, with emphasis on its connection to graph representations. We observe that constant-cost randomized communication problems are equivalent to hereditary (i.e.
Nathaniel Harms +2 more
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On the Automatic Analysis of the Practical Resistance of Obfusting Transformations
Моделирование и анализ информационных систем, 2019 A method is developed for assessing the practical persistence of obfuscating transformations of programs based on the calculation of the similarity index for the original, obfuscated and deobfuscated programs.
Petr D. Borisov, Yu. V. Kosolapov
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Induced Embeddings into Hamming Graphs.
, 2017 Let d be a positive integer. Can a given graph G be realized in R^d so that vertices are mapped to distinct points, two vertices being adjacent if and only if the corresponding points lie on a common line that is parallel to some axis? Graphs admitting such realizations have been studied in the literature for decades under different names.
Martin Milanic +2 more
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Bootstrap percolation on the Hamming graphs
Discrete MathematicsThe $r$-edge bootstrap percolation on a graph is an activation process of the edges. The process starts with some initially activated edges and then, in each round, any inactive edge whose one of endpoints is incident to at least $r$ active edges becomes activated.
Meysam Miralaei +2 more
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