Results 11 to 20 of about 7,385 (154)
On the Unitary Cayley Graph of a Ring [PDF]
The Electronic Journal of Combinatorics, 2012 Let $R$ be a ring with identity. The unitary Cayley graph of a ring $R$, denoted by $G_{R}$, is the graph, whose vertex set is $R$, and in which $\{x,y\}$ is an edge if and only if $x-y$ is a unit of $R$. In this paper we find chromatic, clique and independence number of $G_{R}$, where $R$ is a finite ring.
Kiani, Dariush +1 more
openaire +3 more sources
On Laplacian spectrum of unitary Cayley graphs [PDF]
Acta Universitatis Sapientiae, Informatica, 2021 Abstract Let R be a commutative ring with unity 1 ≠ 0 and let R× be the set of all unit elements of R. The unitary Cayley graph of R, denoted by GR = Cay(R, R×), is a simple graph whose vertex set is R and there is an edge between two distinct vertices x and y of R if and only if x − y ∈ R×.
Pirzada S., Barati Z., Afkhami M.
openaire +3 more sources
On the Unitary Cayley Graph of a Finite Ring [PDF]
The Electronic Journal of Combinatorics, 2009 We study the unitary Cayley graph associated to an arbitrary finite ring, determining precisely its diameter, girth, eigenvalues, vertex and edge connectivity, and vertex and edge chromatic number. We also compute its automorphism group, settling a question of Klotz and Sander. In addition, we classify all planar graphs and perfect graphs within this
Akhtar, Reza +6 more
openaire +3 more sources
Status Sombor Indices of Unitary Cayley Graph
Indian Journal Of Science And TechnologyObjectives: The objective of the study is to obtain the values of status Sombor indices for the unitary Cayley graph. Methods: The unitary Cayley graph 𝑋𝑛 has vertex set 𝑍𝑛 = {0, 1, 2, ...𝑛 − 1}. Vertices a, and b are adjacent, if 𝑔𝑐𝑑(𝑎 − 𝑏, 𝑛) = 1. The status 𝜎 (𝑢) of a vertex u in a graph, G is the sum of distances of all other vertices from u in 𝐺 ...
Syeda Asma Kauser, Mashaer Alsaeedi
openaire +2 more sources
The unitary Cayley graph of a semiring
Discrete Mathematics, 2023 We study the unitary Cayley graph of a matrix semiring. We find bounds for its diameter, clique number and independence number, and determine its girth. We also find the relationship between the diameter and the clique number of a unitary Cayley graph of a semiring $S$ and a matrix semiring over $S$.
David Dolžan
openaire +4 more sources
A New Graphical Representation of the Old Algebraic Structure
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 The most recent advancements in algebra and graph theory enable us to ask a straightforward question: what practical use does this graph connected with a mathematical system have in the real world? With the use of algebraic approaches, we may now tackle a wide range of graph theory‐related problems.
Muhammad Nadeem +4 more
wiley +1 more source
Hyperbolic generalized triangle groups, property (T) and finite simple quotients
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3577-3637, December 2022., 2022 Abstract We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan's property (T). Some of them are significantly shorter than the previously known shortest examples. Moreover, we show that some of those hyperbolic Kazhdan groups possess finite simple quotient groups of arbitrarily large rank; they constitute ...
Pierre‐Emmanuel Caprace +3 more
wiley +1 more source
Search Algorithm Based on Permutation Group by Quantum Walk on Hypergraphes
Chinese Journal of Electronics, Volume 31, Issue 4, Page 626-634, July 2022., 2022 Because a significant number of algorithms in computational science include search challenges and a large number of algorithms that can be transformed into search problems have garnered significant attention, especially the time rate and accuracy of search, a quantum walk search algorithm on hypergraphs, whose aim is to reduce time consumption and ...
Yaoyao JIANG +3 more
wiley +1 more source
On the Energy of Unitary Cayley Graphs [PDF]
The Electronic Journal of Combinatorics, 2009 In this note we obtain the energy of unitary Cayley graph $X_{n}$ which extends a result of R. Balakrishnan for power of a prime and also determine when they are hyperenergetic. We also prove that ${E(X_{n})\over 2(n-1)}\geq{2^{k}\over 4k}$, where $k$ is the number of distinct prime divisors of $n$.
Ramaswamy, H. N., Veena, C. R.
openaire +2 more sources
[Retracted] Roughness in Hypervector Spaces
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 This paper examines rough sets in hypervector spaces and provides a few examples and results in this regard. We also investigate the congruence relations‐based unification of rough set theory in hypervector spaces. We introduce the concepts of lower and upper approximations in hypervector spaces.
Nabilah Abughazalah +3 more
wiley +1 more source