scholarly journals Super H -Antimagic Total Covering for Generalized Antiprism and Toroidal Octagonal Map

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Amir Taimur ◽  
Gohar Ali ◽  
Muhammad Numan ◽  
Adnan Aslam ◽  
Kraidi Anoh Yannick
Keyword(s):  
Arithmetic Sequence ◽  
Total Graph ◽  
Bijective Function ◽  
Positive Integers

Let G be a graph and H ⊆ G be subgraph of G . The graph G is said to be a , d - H antimagic total graph if there exists a bijective function f : V H ∪ E H ⟶ 1,2,3 , … , V H + E H such that, for all subgraphs isomorphic to H , the total H weights W H = W H = ∑ x ∈ V H f x + ∑ y ∈ E H f y forms an arithmetic sequence a , a + d , a + 2 d , … , a + n − 1 d , where a and d are positive integers and n is the number of subgraphs isomorphic to H . An a , d - H antimagic total labeling f is said to be super if the vertex labels are from the set 1,2 , … , | V G . In this paper, we discuss super a , d - C 3 -antimagic total labeling for generalized antiprism and a super a , d - C 8 -antimagic total labeling for toroidal octagonal map.

scholarly journals On(a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Martin Bača ◽  
Andrea Semaničová-Feňovčíková ◽  
Tao-Ming Wang ◽  
Guang-Hui Zhang
Keyword(s):  
Regular Graphs ◽  
Open Problems ◽  
Arithmetic Sequence ◽  
Bijective Mapping ◽  
Vertex Weight ◽  
Positive Integers ◽  
Edge Labeling

An(a,s)-vertex-antimagic edge labeling(or an(a,s)-VAElabeling, for short) ofGis a bijective mapping from the edge setE(G)of a graphGto the set of integers1,2,…,|E(G)|with the property that the vertex-weights form an arithmetic sequence starting fromaand having common differences, whereaandsare two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. A graph is called(a,s)-antimagic if it admits an(a,s)-VAElabeling. In this paper, we investigate the existence of(a,1)-VAE labeling for disconnected 3-regular graphs. Also, we define and study a new concept(a,s)-vertex-antimagic edge deficiency, as an extension of(a,s)-VAE labeling, for measuring how close a graph is away from being an(a,s)-antimagic graph. Furthermore, the(a,1)-VAE deficiency of Hamiltonian regular graphs of even degree is completely determined. More open problems are mentioned in the concluding remarks.

scholarly journals A Super (A,D)-Bm-Antimagic Total Covering of Ageneralized Amalgamation of Fan Graphs

CAUCHY ◽  
2017 ◽  
Vol 4 (4) ◽  
pp. 146
Author(s):  
Ika Hesti Agustin
Keyword(s):  
Arithmetic Progression ◽  
Total Graph ◽  
Bijective Function

<p>All graph in this paper are finite, simple and undirected. Let <em>G, H </em>be two graphs. A graph <em>G </em>is said to be an (<em>a,d</em>)-<em>H</em>-antimagic total graph if there exist a bijective function <em> </em>such that for all subgraphs <em>H’ </em>isomorphic to <em>H</em>, the total <em>H</em>-weights form an arithmetic progression  where <em>a, d &gt; </em>0 are integers and <em>m </em>is the number of all subgraphs <em>H’ </em>isomorphic to <em>H</em>. An (<em>a, d</em>)-<em>H</em>-antimagic total labeling <em>f </em>is called super if the smallest labels appear in the vertices. In this paper, we will study a super (<em>a, d</em>)-<em>B<sub>m</sub></em>-antimagicness of a connected and disconnected generalized amalgamation of fan graphs on which a path is a terminal.</p>

Total graph of the ring ℤn × ℤm

2015 ◽  
Vol 07 (01) ◽  
pp. 1550004 ◽  
Author(s):  
Alpesh M. Dhorajia
Keyword(s):  
Commutative Ring ◽  
Undirected Graph ◽  
Clique Number ◽  
Total Graph ◽  
Fundamental Properties ◽  
Zero Divisors ◽  
Independent Number ◽  
Positive Integers

Let R be a commutative ring and Z(R) be the set of all zero-divisors of R. The total graph of R, denoted by T Γ(R), is the (undirected) graph with vertices set R. For any two distinct elements x, y ∈ R, the vertices x and y are adjacent if and only if x + y ∈ Z(R). In this paper, we obtain certain fundamental properties of the total graph of ℤn × ℤm, where n and m are positive integers. We determine the clique number and independent number of the total graph T Γ(ℤn × ℤm).

scholarly journals Super (a, d)-H-antimagic labeling of subdivided graphs

2018 ◽  
Vol 16 (1) ◽  
pp. 688-697
Author(s):  
Amir Taimur ◽  
Muhammad Numan ◽  
Gohar Ali ◽  
Adeela Mumtaz ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Simple Graph ◽  
Arithmetic Sequence ◽  
Antimagic Labeling ◽  
Bijective Function

AbstractA simple graphG= (V,E) admits anH-covering, if every edge inE(G) belongs to a subgraph ofGisomorphic toH. A graphGadmitting anH-covering is called an (a,d)-H-antimagic if there exists a bijective functionf:V(G) ∪E(G) → {1, 2, …, |V(G)| + |E(G)|} such that for all subgraphsH′ isomorphic toHthe sums ∑v∈V(H′)f(v) + ∑e∈E(H′)f(e) form an arithmetic sequence {a,a+d, …,a+ (t− 1)d}, wherea> 0 andd≥ 0 are integers andtis the number of all subgraphs ofGisomorphic toH. Moreover, if the vertices are labeled with numbers 1, 2, …, |V(G)| the graph is called super. In this paper we deal with super cycle-antimagicness of subdivided graphs. We also prove that the subdivided wheel admits an (a,d)-cycle-antimagic labeling for somed.

scholarly journals PELABELAN SELIMUT TOTAL SUPER (a,d)-H ANTIMAGIC PADA GRAPH LOBSTER BERATURAN L_n (q,r)

2017 ◽  
Vol 6 (2) ◽  
pp. 143
Author(s):  
TIRA CATUR ROSALIA ◽  
LUH PUTU IDA HARINI ◽  
KARTIKA SARI
Keyword(s):  
Connected Graph ◽  
Literature Study ◽  
Injective Function ◽  
Graph Labelling ◽  
Bijective Function ◽  
Positive Integers

Graph labelling is a function that maps graph elements to positive integers. A covering of  graph  is  family subgraph from , for  with integer k. Graph  admits  covering if for every subgraph  is isomorphic to a graph  . A connected graph  is an - antimagic if there are positive integers  and bijective function  such that there are injective function , defined by  with . The purpose of this research is to determine a total super  antimagic covering on lobster graph . The method of this research is literature study method. It is obtained that there are a total super  antimagic covering for  on lobster graph  with integer and even number .  

Sums of Reciprocal Powers of Terms in Arithmetic Sequence

1963 ◽  
Vol 6 (1) ◽  
pp. 109-112
Author(s):  
E. L. Whitney
Keyword(s):  
Bernoulli Numbers ◽  
Euler Numbers ◽  
Arithmetic Sequence ◽  
Simple Method ◽  
Image Position ◽  
Positive Integers

A note by N. Kimura gives the sumsexplicitly linearly interms of the sums for positive integers p.We note here that by a similar simple method, the Bernoulli numbers and Euler numbers may be related similarly to these sums.

Domination in total graphs of small rings

2016 ◽  
Vol 08 (04) ◽  
pp. 1650069
Author(s):  
Alpesh M. Dhorajia ◽  
Jimmy M. Morzaria
Keyword(s):  
Commutative Ring ◽  
Domination Number ◽  
Total Graph ◽  
Zero Divisors ◽  
Positive Integers

Let [Formula: see text] be a commutative ring and [Formula: see text] be its set of zero divisors. The total graph of [Formula: see text] (introduced by Anderson and Badawi) denoted by [Formula: see text]. For any positive integers [Formula: see text] and [Formula: see text] we obtain the domination number of the total graph of [Formula: see text]. We also obtain various domination parameters including [Formula: see text] and [Formula: see text]. Finally we explore domination parameters in the complement of the total graph [Formula: see text].

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.

Language, procedures, and the non-perceptual origin of natural number concepts

2016 ◽  
Author(s):  
David Barner
Keyword(s):  
General Framework ◽  
Ad Hoc ◽  
Building Blocks ◽  
Number Words ◽  
Linguistic Markers ◽  
Logical Foundations ◽  
Large Numbers ◽  
Perceptual Representations ◽  
Positive Integers ◽  
Perceptual Systems

Perceptual representations – e.g., of objects or approximate magnitudes –are often invoked as building blocks that children combine with linguisticsymbols when they acquire the positive integers. Systems of numericalperception are either assumed to contain the logical foundations ofarithmetic innately, or to supply the basis for their induction. Here Ipropose an alternative to this general framework, and argue that theintegers are not learned from perceptual systems, but instead arise toexplain perception as part of language acquisition. Drawing oncross-linguistic data and developmental data, I show that small numbers(1-4) and large numbers (~5+) arise both historically and in individualchildren via entirely distinct mechanisms, constituting independentlearning problems, neither of which begins with perceptual building blocks.Specifically, I propose that children begin by learning small numbers(i.e., *one, two, three*) using the same logical resources that supportother linguistic markers of number (e.g., singular, plural). Several yearslater, children discover the logic of counting by inferring the logicalrelations between larger number words from their roles in blind countingprocedures, and only incidentally associate number words with perception ofapproximate magnitudes, in an *ad hoc* and highly malleable fashion.Counting provides a form of explanation for perception but is not causallyderived from perceptual systems.

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

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