Results 51 to 60 of about 167 (114)
On the Clean Graph of Commutative Artinian Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.For a commutative Artinian ring R with unity, the clean graph Cl(R) is a graph with vertices in the form of an ordered pair (e, u), where e is an idempotent and u is a unit of ring R, respectively. Two distinct vertices (e, u) and (f, v) are adjacent in Cl(R) if and only if ef = fe = 0 or uv = vu = 1.
R. Singh +3 more
wiley +1 more source
Perfect codes in power graphs of finite groups
Open Mathematics, 2017 The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the ...
Ma Xuanlong +4 more
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Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.This article explores numerous significant additive topological indices based on degrees for linear functional graphs over finite‐dimensional vector spaces. Specifically, we derive some unique topological indices, such as the eccentricity‐based indices and the Wiener index.
Vinnarasi L. +4 more
wiley +1 more source
On finite presentability of direct products of semigroups [PDF]
, 2000 A finite semigroup S is said to preserve finite generation (resp., presentability) in direct products, provided that, for every infinite semigroup T, the direct product S x T is finitely generated (resp., finitely presented) if and only if T is finitely ...
Ruskuc, Nikola, Araujo, IM
core
The non-commuting graph of a non-central hypergroup
Open Mathematics, 2019 The aim of this paper is to construct and study the properties of a certain graph associated with a non-central hypergroup, i.e. a hypergroup having non-commutative the associated fundamental group.
Iranmanesh Mahdiyeh +2 more
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Ideal‐Based Quasi Cozero Divisor Graph of a Commutative Ring
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let R be a commutative ring with identity and I be an ideal of R. The zero‐divisor graph of R with respect to I, denoted by ΓI(R), is the graph whose vertices are the set {x ∈ R∖I |xy ∈ I for some y ∈ R∖I} with distinct vertices x and y are adjacent if and only if xy ∈ I.
Faranak Farshadifar, Huadong Su
wiley +1 more source
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
A framework unifying some bijections for graphs and its connection to Lawrence polytopes [PDF]
Let \(G\) be a connected graph. The Jacobian group (also known as the Picard group or sandpile group) of \(G\) is a finite abelian group whose cardinality equals the number of spanning trees of \(G\).
Ding, Changxin
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Open Mathematics, 2020 A Cayley graph Γ\Gamma on a group G is called a dual Cayley graph on G if the left regular representation of G is a subgroup of the automorphism group of Γ\Gamma (note that the right regular representation of G is always an automorphism group of Γ ...
Pan Jiangmin
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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
wiley +1 more source