scholarly journals Prime labeling of line and splitting graph of brush graph

2021 ◽  
Vol 2106 (1) ◽  
pp. 012030
Author(s):  
F Fran ◽  
D R Putra ◽  
M Pasaribu
Keyword(s):  
Prime Graph ◽  
Bijective Function ◽  
Prime Labeling ◽  
Splitting Graph

Abstract A bijective function f from V(G) to {1,2,…, n} be a prime labeling of a graph G with n order if for every u, v ∈ V(G) such that e = uv ∈ E(G), f(u) and f(v) relatively prime. A prime graph is a graph which admits prime labeling. In this study, we investigate and conclude that the line and splitting graph of the brush graph is a prime graph.

scholarly journals On odd prime labeling of graphs

2020 ◽  
Vol 3 (3) ◽  
pp. 33-40
Author(s):  
Maged Zakaria Youssef ◽  
◽  
Zainab Saad Almoreed ◽  
Keyword(s):  
Necessary Conditions ◽  
Prime Graph ◽  
Prime Graphs ◽  
Vertex Set ◽  
Prime Labeling

In this paper we give a new variation of the prime labeling. We call a graph \(G\) with vertex set \(V(G)\) has an odd prime labeling if its vertices can be labeled distinctly from the set \(\big\{1, 3, 5, ...,2\big|V(G)\big| -1\big\}\) such that for every edge \(xy\) of \(E(G)\) the labels assigned to the vertices of \(x\) and \(y\) are relatively prime. A graph that admits an odd prime labeling is called an <i>odd prime graph</i>. We give some families of odd prime graphs and give some necessary conditions for a graph to be odd prime. Finally, we conjecture that every prime graph is odd prime graph.

scholarly journals Prime Labeling of Jahangir Graphs

2018 ◽  
Vol 7 (4.10) ◽  
pp. 389
Author(s):  
Anantha Lakshmi. ◽  
Jayalakshmi. K ◽  
Madhavi T
Keyword(s):  
Prime Number ◽  
Prime Graph ◽  
Graph Operations ◽  
Prime Labeling ◽  
Jahangir Graph

The paper investigates prime labeling of Jahangir graph Jn,m   for n ≥ 2, m ≥ 3 provided that nm is even. We discuss prime labeling of some graph operations viz. Fusion, Switching and Duplication to prove that the Fusion of two vertices v1 and vk where k is odd in a Jahangir graph Jn,m results to prime graph provided that the product nm is even and is relatively prime to k. The Fusion of two vertices vnm + 1 and vk for any k in Jn, m is prime. The switching of vk in the cycle Cnm of the Jahangir graph Jn,m  is a prime graph provided that nm+1 is a prime number and the switching of vnm+1 in Jn, m is also a prime graph .Duplicating of vk, where k is odd integer and nm + 2 is relatively prime to k,k+2 in Jn,m is a prime graph.  

COMBINATORIAL POLYNOMIALLY COMPUTABLE CHARACTERISTICS OF SUBSTITUTIONS AND THEIR PROPERTIES

2020 ◽  
Vol 7 (2) ◽  
pp. 34-41
Author(s):  
VLADIMIR NIKONOV ◽  
◽  
ANTON ZOBOV ◽  
Keyword(s):  
Mathematical Expectation ◽  
Point Of View ◽  
Small Range ◽  
Computational Point ◽  
Wide Range ◽  
Bijective Function ◽  
The Difference ◽  
Element Base ◽  
Selection Of

The construction and selection of a suitable bijective function, that is, substitution, is now becoming an important applied task, particularly for building block encryption systems. Many articles have suggested using different approaches to determining the quality of substitution, but most of them are highly computationally complex. The solution of this problem will significantly expand the range of methods for constructing and analyzing scheme in information protection systems. The purpose of research is to find easily measurable characteristics of substitutions, allowing to evaluate their quality, and also measures of the proximity of a particular substitutions to a random one, or its distance from it. For this purpose, several characteristics were proposed in this work: difference and polynomial, and their mathematical expectation was found, as well as variance for the difference characteristic. This allows us to make a conclusion about its quality by comparing the result of calculating the characteristic for a particular substitution with the calculated mathematical expectation. From a computational point of view, the thesises of the article are of exceptional interest due to the simplicity of the algorithm for quantifying the quality of bijective function substitutions. By its nature, the operation of calculating the difference characteristic carries out a simple summation of integer terms in a fixed and small range. Such an operation, both in the modern and in the prospective element base, is embedded in the logic of a wide range of functional elements, especially when implementing computational actions in the optical range, or on other carriers related to the field of nanotechnology.

scholarly journals Common closed neighbourhood prime labeling

2021 ◽  
Vol 1836 (1) ◽  
pp. 012009
Author(s):  
Rinurwati ◽  
A S Alfiyani
Keyword(s):  
Prime Labeling

scholarly journals Groups with the Same Prime Graph as the Simple Group D n (5)

2014 ◽  
Vol 66 (5) ◽  
pp. 666-677
Author(s):  
A. Babai ◽  
B. Khosravi
Keyword(s):  
Simple Group ◽  
Prime Graph ◽  
Group D

Prime labeling for some bistar related graphs

2021 ◽  
Author(s):  
T. Malathi ◽  
K. Balasangu
Keyword(s):  
Prime Labeling

n-RECOGNITION BY PRIME GRAPH OF THE SIMPLE GROUP PSL(2,q)

2008 ◽  
Vol 07 (06) ◽  
pp. 735-748 ◽  
Author(s):  
BEHROOZ KHOSRAVI
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Prime Number ◽  
Finite Groups ◽  
Prime Graph ◽  
Split Extension ◽  
A Finite Group

Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge if there is an element in G of order pq. It is proved that if p > 11 and p ≢ 1 (mod 12), then PSL(2,p) is uniquely determined by its prime graph. Also it is proved that if p > 7 is a prime number and Γ(G) = Γ(PSL(2,p2)), then G ≅ PSL(2,p2) or G ≅ PSL(2,p2).2, the non-split extension of PSL(2,p2) by ℤ2. In this paper as the main result we determine finite groups G such that Γ(G) = Γ(PSL(2,q)), where q = pk. As a consequence of our results we prove that if q = pk, k > 1 is odd and p is an odd prime number, then PSL(2,q) is uniquely determined by its prime graph and so these groups are characterizable by their prime graph.

CHARACTERIZATION BY PRIME GRAPH OF PGL(2, pk) WHERE p AND k > 1 ARE ODD

2010 ◽  
Vol 20 (07) ◽  
pp. 847-873 ◽  
Author(s):  
Z. AKHLAGHI ◽  
B. KHOSRAVI ◽  
M. KHATAMI
Keyword(s):  
Finite Group ◽  
Group Theory ◽  
Prime Number ◽  
Prime Graph ◽  
Composition Factor ◽  
Simple Groups ◽  
Almost Simple Groups ◽  
Prime Graphs ◽  
A Finite Group ◽  
Nonabelian Composition Factor

Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, p′ are joined by an edge if there is an element in G of order pp′. In [G. Y. Chen et al., Recognition of the finite almost simple groups PGL2(q) by their spectrum, Journal of Group Theory, 10 (2007) 71–85], it is proved that PGL(2, pk), where p is an odd prime and k > 1 is an integer, is recognizable by its spectrum. It is proved that if p > 19 is a prime number which is not a Mersenne or Fermat prime and Γ(G) = Γ(PGL(2, p)), then G has a unique nonabelian composition factor which is isomorphic to PSL(2, p). In this paper as the main result, we show that if p is an odd prime and k > 1 is an odd integer, then PGL(2, pk) is uniquely determined by its prime graph and so these groups are characterizable by their prime graphs.

A dynamic and parallel approach for repetitive prime labeling of XML with MapReduce

2016 ◽  
Vol 73 (2) ◽  
pp. 810-836 ◽  
Author(s):  
Jinhyun Ahn ◽  
Dong-Hyuk Im ◽  
Taewhi Lee ◽  
Hong-Gee Kim
Keyword(s):  
Prime Labeling
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