Results 21 to 30 of about 2,972 (249)
On induced subgraphs of the Hamming graph [PDF]
Journal of Graph Theory, 2020 AbstractIn connection with his solution of the Sensitivity Conjecture, Hao Huang (arXiv: 1907.00847, 2019) asked the following question: Given a graph with high symmetry, what can we say about the smallest maximum degree of induced subgraphs of with vertices, where denotes the size of the largest independent set in ?
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Eccentric Harmonic Index for the Cartesian Product of Graphs
Journal of Mathematics, 2022 Suppose ρ is a simple graph, then its eccentric harmonic index is defined as the sum of the terms 2/ea+eb for the edges vavb, where ea is the eccentricity of the ath vertex of the graph ρ. We symbolize the eccentric harmonic index (EHI) as He=Heρ.
Kamel Jebreen +5 more
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Hamming index of graphs with respect to its incidence matrix
Indonesian Journal of Combinatorics, 2022 Let B(G) be the incidence matrix of a graph G. The row in B(G)corresponding to a vertex v, denoted by s(v) is the string which belongs to ℤm2, a set of m-tuples over a field of order two.
Harishchandra S. Ramane +6 more
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Arithmetic completely regular codes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 In this paper, we explore completely regular codes in the Hamming graphs and related graphs. Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression.
Jacobus Koolen +3 more
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s-Elusive codes in Hamming graphs [PDF]
Designs, Codes and Cryptography, 2021 A code is a subset of the vertex set of a Hamming graph. The set of $s$-neighbours of a code is the set of all vertices at Hamming distance $s$ from their nearest codeword. A code $C$ is $s$-elusive if there exists a distinct code $C'$ that is equivalent to $C$ under the full automorphism group of the Hamming graph such that $C$ and $C'$ have the same ...
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Total mutual-visibility in Hamming graphs [PDF]
Opuscula MathematicaIf \(G\) is a graph and \(X \subseteq V(G)\), then \(X\) is a total mutual-visibility set if every pair of vertices \(x\) and \(y\) of \(G\) admits the shortest \(x,y\)-path \(P\) with \(V(P) \cap X \subseteq \{x,y\}\).
Csilla Bujtás +2 more
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The improved hamming number method to detect isomorphism for kinematic chain with multiple joints
Journal of Advanced Mechanical Design, Systems, and Manufacturing, 2017 During the process of kinematic structure enumeration using graph theory, isomorphism identification of graphs is an important and complicated problem.
Wei SUN, Jianyi KONG, Liangbo SUN
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ON DISTANCE–REGULAR GRAPHS OF DIAMETER 3 WITH EIGENVALUE \(\theta=1\)
Ural Mathematical Journal, 2022 For a distance-regular graph \(\Gamma\) of diameter 3, the graph \(\Gamma_i\) can be strongly regular for \(i=2\) or 3. J.Kulen and co-authors found the parameters of a strongly regular graph \(\Gamma_2\) given the intersection array of the graph ...
Alexander A. Makhnev +2 more
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How Long Can One Bluff in the Domination Game?
Discussiones Mathematicae Graph Theory, 2017 The domination game is played on an arbitrary graph G by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise.
Brešar Boštan +3 more
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Perfect 2‐colorings of Hamming graphs [PDF]
Journal of Combinatorial Designs, 2021 AbstractWe consider the problem of existence of perfect 2‐colorings (equitable 2‐partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs and colorings that are necessary for their existence. Next we observe known constructions of perfect colorings and propose some new ones giving new parameters. At last, we
Evgeny A. Bespalov +4 more
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