• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.117-132
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• 2022

Reverse edge magic(REM) labeling of the graph G = (V, E) is a bijection of vertices and edges to a set of numbers from the set, defined by λ : V ∪ E → {1, 2, 3, …, |V| + |E|} with the property that for every xy ∈ E, constant k is the weight of equals to a xy, that is λ(xy) - [λ(x) + λ(x)] = k for some integer k. We given the construction of REM labeling for the Cartesian Product, Unions of Braids and Unions of Triangular Belts. The Kotzig array used in this paper is the 3 × (2r + 1) kotzig array. we test the konow results about REM labelling that are related to the new results we found.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.445-456
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• 2024

A power cordial labeling of a graph G = (V (G), E(G)) is a bijection f : V (G) → {1, 2, ..., |V (G)|} such that an edge e = uv is assigned the label 1 if f(u) = (f(v))ⁿ or f(v) = (f(u))ⁿ, for some n ∈ ℕ ∪ {0} {0} and the label 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we study power cordial labeling and investigate power cordial labeling for some standard graph families.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.435-445
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• 2017

Let D be a directed graph with p vertices and q arcs. A vertex out-magic total labeling is a bijection f from $V(D){\cup}A(D){\rightarrow}\{1,2,{\ldots},p+q\}$ with the property that for every $v{\in}V(D)$, $f(v)+\sum_{u{\in}O(v)}f((v,u))=k$, for some constant k. Such a labeling is called a V-super vertex out-magic total labeling (V-SVOMT labeling) if $f(V(D))=\{1,2,3,{\ldots},p\}$. A digraph D is called a V-super vertex out-magic total digraph (V-SVOMT digraph) if D admits a V-SVOMT labeling. In this paper, we provide a method to find the most vital nodes in a network by introducing the above labeling and we study the basic properties of such labelings for digraphs. In particular, we completely solve the problem of finding V-SVOMT labeling of generalized de Bruijn digraphs which are used in the interconnection network topologies.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.673-688
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• 2011

Let $n{\geq}2$ be an even integer. We investigate that if an odd mapping f : X ${\rightarrow}$ Y satisfies the following equation $2_{n-2}C_{\frac{n}{2}-1}rf\(\sum\limits^n_{j=1}{\frac{x_j}{r}}\)\;+\;{\sum\limits_{i_k{\in}\{0,1\} \atop {{\sum}^n_{k=1}\;i_k={\frac{n}{2}}}}\;rf\(\sum\limits^n_{i=1}(-1)^{i_k}{\frac{x_i}{r}}\)=2_{n-2}C_{{\frac{n}{2}}-1}\sum\limits^n_{i=1}f(x_i),$ then f : X ${\rightarrow}$ Y is additive, where $r{\in}R$. We also prove the stability in normed group by using shadowing property and the Hyers-Ulam stability of the functional equation in Banach spaces and in Banach modules over unital C-algebras. As an application, we show that every almost linear bijection h : A ${\rightarrow}$ B of unital $C^*$-algebras A and B is a $C^*$-algebra isomorphism when $h(\frac{2^s}{r^s}uy)=h(\frac{2^s}{r^s}u)h(y)$ for all unitaries u ${\in}$ A, all y ${\in}$ A, and s = 0, 1, 2,....

• East Asian mathematical journal
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• v.23 no.1
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• pp.23-36
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• 2007

In this paper we consider the fuzzy ideals of N-group G where N is a nearring. We introduce fuzzy ideal ${\theta}_{\mu}$ of the quotient N-group $G/{\mu}$ with respect to a fuzzy ideal $\mu$ of G. If $\mu$ is a fuzzy ideal of G and $\theta$ a fuzzy ideal of $G/{\mu}$ such that ${\theta}_{\mu}\;{\subseteq}\;{\theta}$ and ${\theta}_{\mu}(0)\;=\;{\theta}(0)$, then corresponding ${\sigma}_{\theta}\;:\;G\;{\rightarrow}\;[0,\;1]$ is defined and proved that it is a fuzzy ideal of G such that ${\mu}\;{\subseteq}\;{\sigma}_{\theta}$ and ${\mu}(0)\;=\;{\sigma}_{\theta}(0)$. We also prove some results on homomorphisms and fuzzy ideals of N-groups. The image and preimage of fuzzy ideal $\mu$ under N-group homomorphism were studied. Finally it is obtained that if $f\;:\;G\;{\rightarrow}\;G^1$ is an epimorphism of N-groups, then there is an order preserving bijection between the fuzzy ideals of $G^1$ and the fuzzy ideals of G that are constant on kerf. Some examples related to these concepts were illustrated.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.657-668
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• 2016

Given a partition ${\lambda}=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_l)$ of a positive integer n, let Tab(${\lambda}$, k) be the set of all tabloids of shape ${\lambda}$ whose weights range over the set of all k-compositions of n and ${\mathcal{OP}}^k_{\lambda}_{rev}$ the set of all ordered partitions into k blocks of the multiset $\{1^{{\lambda}_l}2^{{\lambda}_{l-1}}{\cdots}l^{{\lambda}_1}\}$. In [2], Butler introduced an inversion-like statistic on Tab(${\lambda}$, k) to show that the rank-selected $M{\ddot{o}}bius$ invariant arising from the subgroup lattice of a finite abelian p-group of type ${\lambda}$ has nonnegative coefficients as a polynomial in p. In this paper, we introduce an inversion-like statistic on the set of ordered partitions of a multiset and construct an inversion-preserving bijection between Tab(${\lambda}$, k) and ${\mathcal{OP}}^k_{\hat{\lambda}}$. When k = 2, we also introduce a major-like statistic on Tab(${\lambda}$, 2) and study its connection to the inversion statistic due to Butler.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.617-630
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• 2011

Let X, Y be vector spaces, and let r be 2 or 4. It is shown that if an odd mapping $f:X{\rightarrow}Y$ satisfies the functional equation $${\hspace{50}}rf(\frac{\sum_{j=1}^{d}\;x_j} {r})+\;{\sum\limits_{\iota(j)=0,1 \atop {\sum_{j=1}^{d}}\;{\iota}(j)=l}}\;rf(\frac{\sum_{j=1}^{d}{(-1)^{\iota(j)}x_j}}{r}) \\({\ddag}){\hspace{160}}=(_{d-1}C_l-_{d-1}C_{l-1}+1)\;{\sum\limits_{j=1}^{d}\;f(x_j)}$$ then the odd mapping $f:X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation in Banach modules over a unital $C^*$-algebra. As an application, we show that every almost linear bijection $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ of a unital $C^*$-algebra ${\mathcal{A}}$ onto a unital $C^*$-algebra ${\mathcal{B}}$ is a $C^*$-algebra isomorphism when $h(2^nuy)=h(2^nu)h(y)$ for all unitaries $u{\in}{\mathcal{A}}$, all $y{\in}{\mathcal{A}}$, and $n=0,1,2,{\cdots}$.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• Journal of the Institute of Convergence Signal Processing
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• v.23 no.3
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• pp.143-149
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• 2022

This excerpt delineates a quantitative measure of relationship between a research title and its respective abstract extracted from different journal articles documented through a Korean Citation Index (KCI) database published through various journals. In this paper, we propose a machine learning-based similarity metric that does not assume normality on dataset, realizes the imbalanced dataset problem, and zero-variance problem that affects most of the rule-based algorithms. The advantage of using this algorithm is that, it eliminates the limitations experienced by Pearson correlation coefficient (r) and additionally, it solves imbalanced dataset problem. A total of 107 journal articles collected from the database were used to develop a corpus with authors, year of publication, title, and an abstract per each. Based on the experimental results, the proposed algorithm achieved high correlation coefficient values compared to others which are cosine similarity, euclidean, and pearson correlation coefficients by scoring a maximum correlation of 1, whereas others had obtained non-a-number value to some experiments. With these results, we found that an effective title must have high correlation coefficient with the respective abstract.

• Communications of Mathematical Education
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• v.27 no.3
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• pp.267-281
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• 2013

In this paper, we explore the possibility that ladder diagram games can be used for the introduction of the function and composite function. A ladder diagram with at most one rung is a bijection. Thus a ladder diagram with r rungs is the composition of r one-to-one correspondence. In this paper, we use ladder diagrams to give simple proofs of some fundamental facts about one-to-one correspondence. Also, we suggest Story-telling for introduction of function in middle school and high school. The ladder diagram approach to one-to-one correspondence not only grabs our students' attention, but also facilitates their understanding of the concept of functions.