Results 51 to 60 of about 1,357 (88)
On the Number of Hamiltonian Groups [PDF]
, 2005 Finite hamiltonian groups are counted. The sequence of numbers of all groups of order $n$ all whose subgroups are normal and the sequence of numbers of all groups of order less or equal to $n$ all whose subgroups are normal are presented.Comment: 6 pages,
Horvat, Boris +2 more
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Existence and Classification of 3‐Regular Symmetric Graphs of Order 6pq With Distinct Primes p and q
Journal of Mathematics, Volume 2025, Issue 1, 2025.A graph Σ is said symmetric if its automorphism group acts transitively on the set of its arc. Let p < q be two distinct prime integers. This paper demonstrates that connected 3‐regular symmetric graphs of order 6pq exist if and only if the pair (p, q) belongs to the set (5, 19), (19, 37), (37, 73), which up to isomorphism there are nine sporadic ones,
Mehdi Alaeiyan +3 more
wiley +1 more source
Note on the product of the largest and the smallest eigenvalue of a graph
Special MatricesIn this note, we use eigenvalue interlacing to derive an inequality between a graph’s maximum degree and its maximum and minimum adjacency eigenvalues. The equality case is fully characterized.
Abiad Aida +2 more
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Finite groups with star-free noncyclic graphs
Open Mathematics, 2019 For a finite noncyclic group G, let Cyc(G) be the set of elements a of G such that 〈a, b〉 is cyclic for each b of G. The noncyclic graph of G is a graph with the vertex set G ∖ Cyc(G), having an edge between two distinct vertices x and y if 〈x, y〉 is not
Ma Xuanlong, Walls Gary L., Wang Kaishun
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On divisibility graph for simple Zassenhaus groups [PDF]
, 2014 The divisibility graph $D(G)$ for a finite group $G$ is a graph with vertex set $cs~(G)\setminus\{1\}$ where $cs~(G)$ is the set of conjugacy class sizes of $G$. Two vertices $a$ and $b$ are adjacent whenever $a$ divides $b$ or $b$ divides $a$.
A. Abdolghafourian +2 more
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Enumerating Problems Concerning Endomorphisms of Double Vertex Wheel Graphs
Journal of Mathematics, Volume 2024, Issue 1, 2024.We can define six classes of endomorphisms on a graph, and they always form a chain based on set inclusion. The concepts of endomorphism type and endomorphism spectrum were introduced by Böttcher and Knauer in 1992. They provided a systematic and organized approach to study endomorphisms of graphs.
Yu Li, Hailong Hou, Kaidi Xu, Huadong Su
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End-regular and End-orthodox generalized lexicographic products of bipartite graphs
Open Mathematics, 2016 A graph X is said to be End-regular (End-orthodox) if its endomorphism monoid End(X) is a regular (orthodox) semigroup. In this paper, we determine the End-regular and the End-orthodox generalized lexicographic products of bipartite graphs.
Gu Rui, Hou Hailong
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Journal of Mathematics, Volume 2024, Issue 1, 2024.Symmetry properties are of vital importance for graphs. The famous Cayley graph is a good mathematical model as its high symmetry. The normality of the graph can well reflect the symmetry of the graph. In this paper, we characterize the normality of the direct product of Cayley graphs and give a sufficient and necessary condition for the direct product
Li Wang +3 more
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Cyclic Partitions of Complete and Almost Complete Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2022 We consider cyclic partitions of the complete k-uniform hypergraph on a finite set V, minus a set of s edges, s ≥ 0. An s-almost t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation ...
Dilbarjot, Gosselin Shonda Dueck
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On θ-commutators and the corresponding non-commuting graphs
Open Mathematics, 2017 The θ-commutators of elements of a group with respect to an automorphism are introduced and their properties are investigated. Also, corresponding to θ-commutators, we define the θ-non-commuting graphs of groups and study their correlations with other ...
Shalchi S., Erfanian A., Farrokhi DG M.
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