• Title/Summary/Keyword: Graph Labeling

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A NOTE ON VERTEX PAIR SUM k-ZERO RING LABELING

  • ANTONY SANOJ JEROME;K.R. SANTHOSH KUMAR;T.J. RAJESH KUMAR
    • Journal of applied mathematics & informatics
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    • v.42 no.2
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    • pp.367-377
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    • 2024
  • Let G = (V, E) be a graph with p-vertices and q-edges and let R be a finite zero ring of order n. An injective function f : V (G) → {r1, r2, , rk}, where ri ∈ R is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.

GROUP S3 CORDIAL REMAINDER LABELING FOR PATH AND CYCLE RELATED GRAPHS

  • LOURDUSAMY, A.;WENCY, S. JENIFER;PATRICK, F.
    • Journal of applied mathematics & informatics
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    • v.39 no.1_2
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    • pp.223-237
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    • 2021
  • Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.

ODD-EVEN GRACEFUL GRAPHS

  • Sridevi, R.;Navaneethakrishnan, S.;Nagarajan, A.;Nagarajan, K.
    • Journal of applied mathematics & informatics
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    • v.30 no.5_6
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    • pp.913-923
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    • 2012
  • The Odd-Even graceful labeling of a graph G with $q$ edges means that there is an injection $f:V (G)$ to $\{1,3,5,{\cdots},2q+1\}$ such that, when each edge $uv$ is assigned the label ${\mid}f(u)-f(v){\mid}$, the resulting edge labels are $\{2,4,6,{\cdots},2q\}$. A graph which admits an odd-even graceful labeling is called an odd-even graceful graph. In this paper, we prove that some well known graphs namely $P_n$, $P_n^+$, $K_{1,n}$, $K_{1,2,n}$, $K_{m,n}$, $B_{m,n}$ are Odd-Even graceful.

SOME 4-TOTAL PRIME CORDIAL LABELING OF GRAPHS

  • PONRAJ, R.;MARUTHAMANI, J.;KALA, R.
    • Journal of applied mathematics & informatics
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    • v.37 no.1_2
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    • pp.149-156
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    • 2019
  • Let G be a (p, q) graph. Let $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ be a map where $k{\in}{\mathbb{N}}$ and k > 1. For each edge uv, assign the label gcd(f(u), f(v)). f is called k-Total prime cordial labeling of G if ${\mid}t_f(i)-t_f(j){\mid}{\leq}1$, $i,j{\in}\{1,2,{\ldots},k\}$ where $t_f$(x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of some graphs.

The Research of Q-edge Labeling on Binomial Trees related to the Graph Embedding (그래프 임베딩과 관련된 이항 트리에서의 Q-에지 번호매김에 관한 연구)

  • Kim Yong-Seok
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.42 no.1
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    • pp.27-34
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    • 2005
  • In this paper, we propose the Q-edge labeling method related to the graph embedding problem in binomial trees. This result is able to design a new reliable interconnection networks with maximum connectivity using Q-edge labels as jump sequence of circulant graph. The circulant graph is a generalization of Harary graph which is a solution of the optimal problem to design a maximum connectivity graph consists of n vertices End e edgies. And this topology has optimal broadcasting because of having binomial trees as spanning tree.

GROUP S3 CORDIAL REMAINDER LABELING OF SUBDIVISION OF GRAPHS

  • LOURDUSAMY, A.;WENCY, S. JENIFER;PATRICK, F.
    • Journal of applied mathematics & informatics
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    • v.38 no.3_4
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    • pp.221-238
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    • 2020
  • Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that subdivision of graphs admit a group S3 cordial remainder labeling.

Study on the L(2,1)-labeling problem based on simulated annealing algorithm (Simulated Annealing 알고리즘에 기반한 L(2,1)-labeling 문제 연구)

  • Han, Keun-Hee;Lee, Yong-Jin
    • Journal of the Korean Institute of Intelligent Systems
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    • v.21 no.1
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    • pp.138-144
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    • 2011
  • L(2, 1)-labeling problem of a graph G = (V, E) is a problem to find an efficient way to distribute radio frequencies to various wireless equipments in wireless networks. In this work, we suggest a Simulated Annealing algorithm that can be applied to the L(2, 1)-labeling problem. By applying the suggested algorithm to various graphs we will try to show the efficiency of our algorithm.

The Study on the Upper-bound of Labeling Number for Chordal and Permutation Graphs (코달 및 순열 그래프의 레이블링 번호 상한에 대한 연구)

  • Jeong, Tae-Ui;Han, Geun-Hui
    • The Transactions of the Korea Information Processing Society
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    • v.6 no.8
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    • pp.2124-2132
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    • 1999
  • Given a graph G=(V,E), Ld(2,1)-labeling of G is a function f : V(G)$\longrightarrow$[0,$\infty$) such that, if v1,v2$\in$V are adjacent, $\mid$ f(x)-f(y) $\mid$$\geq$2d, and, if the distance between and is two, $\mid$ f(x)-f(y) $\mid$$\geq$d, where dG(,v2) is shortest distance between v1 and in G. The L(2,1)-labeling number (G) is the smallest number m such that G has an L(2,1)-labeling f with maximum m of f(v) for v$\in$V. This problem has been studied by Griggs, Yeh and Sakai for the various classes of graphs. In this paper, we discuss the upper-bound of ${\lambda}$ (G) for a chordal graph G and that of ${\lambda}$(G') for a permutation graph G'.

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