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Dissertations / Theses on the topic 'Graceful graphs'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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1

Chan, Tsz-lung. "Graceful labelings of infinite graphs." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/hkuto/record/B39332184.

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2

Chan, Tsz-lung, and 陳子龍. "Graceful labelings of infinite graphs." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39332184.

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3

Aftene, Florin. "Vertex-Relaxed Graceful Labelings of Graphs and Congruences." TopSCHOLAR®, 2018. https://digitalcommons.wku.edu/theses/2664.

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A labeling of a graph is an assignment of a natural number to each vertex of a graph. Graceful labelings are very important types of labelings. The study of graceful labelings is very difficult and little has been shown about such labelings. Vertex-relaxed graceful labelings of graphs are a class of labelings that include graceful labelings, and their study gives an approach to the study of graceful labelings. In this thesis we generalize the congruence approach of Rosa to obtain new criteria for vertex-relaxed graceful labelings of graphs. To do this, we generalize Faulhaber’s Formula, which
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4

Cheng, Hee Lin. "Supermagic labeling, edge-graceful labeling and edge-magic index of graphs." HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/280.

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5

Niedzialomski, Amanda Jean. "Consecutive radio labelings and the Cartesian product of graphs." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/4886.

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For k∈{Z}+ and G a simple connected graph, a k-radio labeling f:VG→Z+ of G requires all pairs of distinct vertices u and v to satisfy |f(u)-f(v)|≥ k+1-d(u,v). When k=1, this requirement gives rise to the familiar labeling known as vertex coloring for which each vertex of a graph is labeled so that adjacent vertices have different "colors". We consider k-radio labelings of G when k=diam(G). In this setting, no two vertices can have the same label, so graphs that have radio labelings of consecutive integers are one extreme o
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6

Bournat, Marjorie. "Graceful Degradation and Speculation for Robots in Highly Dynamic Environments." Electronic Thesis or Diss., Sorbonne université, 2019. http://www.theses.fr/2019SORUS035.

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Les systèmes distribués sont des systèmes composés de plusieurs processus communiquants et coopérants ensemble pour résoudre des tâches communes. C’est un modèle générique pour de nombreux systèmes réels comme les réseaux sans fil ou mobiles, les systèmes multiprocesseurs à mémoire partagée, etc. D’un point de vue algorithmique, il est reconnu que de fortes hypothèses (comme l’asynchronisme ou la mobilité) sur de tels systèmes mènent souvent à des résultats d’impossibilité ou à de fortes bornes inférieures sur les complexités. Dans cette thèse, nous étudions des algorithmes qui s’auto-adaptent
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7

Meadows, Adam M. "Decompositions of Mixed Graphs with Partial Orientations of the P4." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1870.

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A decomposition D of a graph H by a graph G is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. A mixed graph on V vertices is an ordered pair (V,C), where V is a set of vertices, |V| = v, and C is a set of ordered and unordered pairs, denoted (x, y) and [x, y] respectively, of elements of V [8]. An ordered pair (x, y) ∈ C is called an arc of (V,C) and an unordered pair [x, y] ∈ C is called an edge of graph (V,C). A path on n vertices is denoted as Pn. A partial orientation on G is obtained by replacing each edge [x,
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8

Jum, Ernest. "The Last of the Mixed Triple Systems." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1876.

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In this thesis, we consider the decomposition of the complete mixed graph on v vertices denoted Mv, into every possible mixed graph on three vertices which has (like Mv) twice as many arcs as edges. Direct constructions are given in most cases. Decompositions of theλ-fold complete mixed graph λMv, are also studied.
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9

Hsu, Yen-Wu, and 許炎午. "Graceful Labelings of Some Special Graphs." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/15033129902556277565.

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碩士<br>淡江大學<br>中等學校教師在職進修數學教學碩士學位班<br>103<br>Let G be a simple graph with q edges. If there exists a function f from V(G) to {0, 1, 2, ..., q} and f is one-to-one. If from f we can get a function g, g : E(G)→{1, 2, ..., q} defined by g(e) =│ f (u) − f (v)│for every edge e = {u, v}∈E(G), and g is a bijective function, then we call f is a graceful labeling of G and the graph G is a graceful graph. Let Cn⊙Pm be the graph obtained by attaching a path Pm to each vertex of an n-cycle Cn. Let Cn⊙[(n－1)Pm∪Pu] be the graph obtained by attaching a path Pu to a vertex of an n-cycle Cn and attaching a pat
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10

WU, SHUN-LIANG, and 吳順良. "On the new constructions of graceful graphs." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/09357296953549363294.

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11

Hong, Lian-Jhih, and 洪連志. "The oriented-k-graceful labelings of graphs." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/8h38p4.

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碩士<br>國立東華大學<br>應用數學系<br>95<br>Given a graph $G$ with $n$ vertices and a function $L:V(G) ightarrow2^{mathbb{N}}$, Let $G$ be a graph with $|V(G)|=n$ and $|E(G)|=m$, a extit{graceful labeling} of is a one-to-one function $f:V(G) ightarrow {0,1,2,...,m}$ such that ${|f(u)-f(v)|:uvin E(G)}={1,2,cdots ,m}$. A graph is graceful if it has a graceful labeling. Given integers $n,k$ with $kgeq 2$, we use $n_{k ext{ }}$to denote the number $n mod k$, and use $n_{/k,i}$ to denote the number $leftlfloor frac{n}{k} ight floor +delta _{i}$, where [ delta _{i}=left{ egin{array}{ll} 1. & ext{if }ileq ((m
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12

Chang, Chi-Nan, and 張吉南. "A Study On Graceful Labelings of Disconnected Graphs." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/92778469461154228156.

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碩士<br>真理大學<br>數理科學研究所<br>89<br>Given a graph G, a graceful labeling f of G is an injection from f:V→{0,1,…,|E|} such that the function f':E→{1,2,3, …,|E|}, defined by f'(uv)=|f(u)-f(v)| for every edge uv in E,is a bijection. In this thesis, we study the graceful labeling for the union of two graphs G1 and G2, where G1 is a path, cycle or P_{a,b} and G2 is a path. We also study graceful labeling for the graph K_{n}\square S_{2^{n-1}- \binom{n}{2}-1}
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13

Lin, Shu-Ching, and 林淑靜. "Graceful Labelings for the Join of two Graphs." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/76900690846489223862.

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碩士<br>淡江大學<br>中等學校教師在職進修數學教學碩士學位班<br>103<br>Let G be a simple graph with m edges. If there is a function f : V(G)→{0,1,2,…,m} and fis one-to-one. From the function f we can get a function g : E(G)→{1,2,…,m}, defined by g(e)=|f(u)-f(v)|, for e={u,v}∈E(G), and g is bijective, then we call f is a graceful labeling and G is a grace graph. In this thesis, we obtain the following results. (1)Let m and n be positive integers. If G is a graph with n vertices and n–1 edges and G is graceful, then GvKm is a graceful graph. (2)Let t be appositive integer. If m=3,4,or 5,then CmvKtis a graceful graph.
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14

Chi, Mu-Yin, та 紀牧音. "On the construction of graphs with graceful labeling and α-labeling". Thesis, 2009. http://ndltd.ncl.edu.tw/handle/14338371713151522221.

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碩士<br>國立交通大學<br>資訊科學與工程研究所<br>98<br>Let G be a simple graph with m edges and let f：V(G) → {0,1, ...,m} be an injection. The vertex labeling is called a graceful labeling if every edge (u,v) is assigned an edge label |f(x)–f(y)|and the resulting edge labels are mutually distinct. A graph possessing a graceful labeling is called a graceful graph. With an additional property that there exists an boundary value k so that for each edge (u,v) either f(u)≤k<f(v) or f(v)≤k<f(u), the graceful labeling is called an α−labeling. One approach about graph labeling is to construct larger graphs from smalle
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15

CHEN, YU-HSIANG, and 陳育祥. "Studies on the Deficiency Problems of Graceful Labeling over Eulerian Graphs." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/87017171363493153009.

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碩士<br>東海大學<br>應用數學系<br>104<br>The following condition (due to A. Rosa) is known to be necessary for an Eulerian graph G admitting a graceful valuation: jE(G)j 0 or 3 (mod 4). The condition is thus sucient if G is a cycle Cn on n vertices. In 1994 J. Abrham and A. Kotzig proved that the 2-regular graph kC4, the disjoint union of k copies of 4-cycles, admits graceful labeling for every positive integer k. In 1996 they also showed that the 2-regular graph Cp and Cq, the disjoint union of Cp and Cq, admits a graceful valuation if p + q 0 or 3 (mod 4). In this thesis we study the notion graceful
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16

Guyer, Michael. "Common Techniques in Graceful Tree Labeling with a New Computational Approach." 2016. http://digital.library.duq.edu/u?/etd,197178.

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The graceful tree conjecture was first introduced over 50 years ago, and to this day it remains largely unresolved. Ideas for how to label arbitrary trees have been sparse, and so most work in this area focuses on demonstrating that particular classes of trees are graceful. In my research, I continue this effort and establish the gracefulness of some new tree types using previously developed techniques for constructing graceful trees. Meanwhile, little work has been done on developing computational methods for obtaining graceful labelings, as direct approaches are computationally infeasible fo
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17

Morgan, David. "Gracefully labelled trees from Skolem and related sequences /." 2001.

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