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Dissertations / Theses on the topic 'Petersen graph'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Crinion, Tim. "Chamber graphs of some geometries related to the Petersen graph." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/chamber-graphs-of-some-geometries-related-to-the-petersen-graph(f481f0af-7c39-4728-8928-571495d1217a).html.

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In this thesis we study the chamber graphs of the geometries ΓpA2nΓ1q, Γp3A7q, ΓpL2p11qq and ΓpL2p25qq which are related to the Petersen graph [4, 13]. In Chapter 2 we look at the chamber graph of ΓpA2nΓ1q and see what minimal paths between chambers look like. Chapter 3 finds and proves the diameter of these chamber graphs and we see what two chambers might look like if they are as far apart as possible. We discover the full automorphism group of the chamber graph. Chapters 4, 5 and 6 focus on the chamber graphs of ΓpL2p11qq,ΓpL2p25qq and Γp3A7q respectively. We ask questions such as what two

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2

Pensaert, William. "Hamilton Paths in Generalized Petersen Graphs." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1198.

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This thesis puts forward the conjecture that for <i>n</i> > 3<i>k</i> with <i>k</i> > 2, the generalized Petersen graph, <i>GP</i>(<i>n,k</i>) is Hamilton-laceable if <i>n</i> is even and <i>k</i> is odd, and it is Hamilton-connected otherwise. We take the first step in the proof of this conjecture by proving the case <i>n</i> = 3<i>k</i> + 1 and <i>k</i> greater than or equal to 1. We do this mainly by means of an induction which takes us from <i>GP</i>(3<i>k</i> + 1, <i>k</i>) to <i>GP</i>(3(<i>k</i> + 2) + 1, <i>k</i> + 2). The induction takes the form of mapping a Hamilton path in

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3

Potanka, Karen Sue. "Groups, Graphs, and Symmetry-Breaking." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36630.

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A labeling of a graph G is said to be r-distinguishing if no automorphism of G preserves all of the vertex labels. The smallest such number r for which there is an r-distinguishing labeling on G is called the distinguishing number of G. The distinguishing set of a group Gamma, D(Gamma), is the set of distinguishing numbers of graphs G in which Aut(G) = Gamma. It is shown that D(Gamma) is non-empty for any finite group Gamma. In particular, D(D<sub>n</sub>) is found where D<sub>n</sub> is the dihedral group with 2n elements. From there, the generalized Petersen graphs, GP(n,k), are defined

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4

Allie, Imran. "Measurements of edge uncolourability in cubic graphs." University of the Western Cape, 2020. http://hdl.handle.net/11394/7869.

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Philosophiae Doctor - PhD<br>The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the Blanusa snarks, to discovering in nite classes of uncolourable cubic graphs such as the Louphekine and Goldberg snarks, to investigating parameters which measure the uncolourability of cubic graphs. These parameters include resistance, oddness and weak oddness, ow resistance, among others. In this thesis, we consider current ideas and problem

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5

Chen, Min. "Vertex coloring of graphs via the discharging method." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14090/document.

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Dans cette thèse, nous nous intéressons à differentes colorations des sommets d’un graphe et aux homomorphismes de graphes. Nous nous intéressons plus spécialement aux graphes planaires et aux graphes peu denses. Nous considérons la coloration propre des sommets, la coloration acyclique, la coloration étoilée, lak-forêt-coloration, la coloration fractionnaire et la version par liste de la plupart de ces concepts.Dans le Chapitre 2, nous cherchons des conditions suffisantes de 3-liste colorabilité des graphes planaires. Ces conditions sont exprimées en termes de sous-graphes interdits et nos ré

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6

Dirino, Kariny de Andrade. "Um estudo sobre álgebras associadas a alguns grafos orientados em níveis." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/7784.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-09-22T11:27:19Z No. of bitstreams: 2 Dissertação - Kariny de Andrade Dirino - 2017.pdf: 1986993 bytes, checksum: fd843aaf3aee361fd3b4dd512828d8f0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-09-22T11:27:47Z (GMT) No. of bitstreams: 2 Dissertação - Kariny de Andrade Dirino - 2017.pdf: 1986993 bytes, checksum: fd843aaf3aee361fd3b4dd512828d8f0 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<

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Sanford, Alice Jewel. "Cycle spectra, automorphic uniqueness, and isomorphism classes of generalized Petersen graphs /." Full text available from ProQuest UM Digital Dissertations, 2005. http://0-proquest.umi.com.umiss.lib.olemiss.edu/pqdweb?index=0&did=1264606591&SrchMode=1&sid=3&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1185199901&clientId=22256.

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8

Cheng, Yi-Jie, and 鄭伊婕. "alpha-Domination of Generalized Petersen Graph." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/27779682628490463135.

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碩士<br>國立交通大學<br>應用數學系所<br>102<br>Let G = (V,E) be a graph with n vertices, m edges and no isolated vertices. For some α with 0 < α ≤ 1 and a set S ⊆ V, we say that S is α−dominating if for all v ∈ V − S, |N(v)∩ S| ≥ α|N(v)|. The size of a smallest such S is called the α−domination number of G denoted by γα(G). For positive integers n and k, the generalized Petersen graph P(n, k) is the graph with vertex set V = {u0, u1, . . ., un−1}∪{v0, v1, . . ., vn−1} and the edge set E = {uiui+1, uivi, vivi+k | i ∈ Zn} where addition is modulo n. Clearly, P(n, k) is a 3-regular graph. In this thesis, w

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9

Yang, Neo, and 楊易鑫. "A Study of the Generalized Petersen Graph and a Novel Graph Y." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/90946261453604898086.

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碩士<br>國立海洋大學<br>電機工程學系<br>90<br>This thesis presents a detailed study of several properties of the generalized Petersen graph, which are considered important to the parallel architectures. Similar to the well-known Petersen graph, the generalized Petersen graph contains two cycles; all the nodes within one cycle are each linked to their counterparts in the other cycle. Each cycle can hold either exactly five nodes or any number of nodes larger than six, according to our study. Besides the detailed analyses of several important properties of the generalized Petersen graph, we also propose a sho

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10

Culos, Garrett James. "Refined Inertias Related to Biological Systems and to the Petersen Graph." Thesis, 2015. http://hdl.handle.net/1828/6525.

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Many models in the physical and life sciences formulated as dynamical systems have a positive steady state, with the local behavior of this steady state determined by the eigenvalues of its Jacobian matrix. The first part of this thesis is concerned with analyzing the linear stability of the steady state by using sign patterns, which are matrices with entries from the set {+,-,0}. The linear stability is related to the allowed refined inertias of the sign pattern of the Jacobian matrix of the system, where the refined inertia of a matrix is a 4-tuple (n+, n_-, ; nz; 2np) with n+ (n_) equal to

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11

MAI, SHIEN, and 買世恩. "The Study For Two Adjacent Vertices Fault-Tolerance Hamiltonian of Generalized Petersen Graph." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/yp3meq.

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碩士<br>國立高雄應用科技大學<br>資訊管理系碩士在職專班<br>106<br>Interconnection networks is usually represented by a graph, and the fault tolerance is an important feature for the interconnection networks, A hamiltonian cycle is a cycle in a graph that visits each vertex exactly once. A graph is 1-node fault tolerance Hamiltonian if is Hamiltonian for any , the hamiltonian of generalized Petersen graph and 1-node fault tolerance hamiltonian of generalized Petersen graph had already been found. In this paper, we will discuss and prove the two adjacent vertices fault-tolerance hamiltonian of Generalized Petersen Gr

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12

Li, Yuan-shin, and 李元馨. "Domination in generalized Petersen graphs." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/25053155376826226509.

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碩士<br>國立中央大學<br>數學研究所<br>99<br>A vertex subset S of a graph G is a dominating set if each vertex in V(G)−S is adjacent to at least one vertex in S. The domination number of G is the cardinality of a minimum dominating set of G, denoted by γ(G). A dominating set S is called an independent dominating set if S is also an independent set. The independent domination number of G is the cardinality of a minimum independent dominating set of G, denoted by γi(G). A dominating set S is called a total dominating set if each vertex v of G is dominated by some vertex u , v of S. The total domination number

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13

Yang, Ching-Han, and 楊京翰. "On (2,1)-total labelings of generalized Petersen graphs." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/79972233238411144854.

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碩士<br>中原大學<br>數學研究所<br>98<br>Let G = (V,E) be a graph. A (2,1)-total labeling of G is a mapping ℓ from V∪E into {0,...,λ}, for some integer λ, such that: (i) if x and y are adjacent vertices then ℓ(x)≠ℓ(y), (ii) if e and f are adjacent edges then ℓ(e)≠ℓ(f), (iii) if an edge e is incident to a vertex x then |ℓ(x)-ℓ(e)|≧2. The minimum λ for which G has a (2,1)-total labeling into {0,...,λ} is denoted by λ^T_2(G). Let n and k be two positive integers. The graph with vertices {u_1,...,u_n} and {v_1,...,v_n} and edges u_iu_(i+1), u_iv_i and v_iv_(i+k), where addition is modulo n is called generaliz

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14

Liu, Chi-Hua, and 劉志華. "On (2,1)-total labeling of generalized Petersen graphs." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/15358918553230042161.

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碩士<br>中原大學<br>應用數學研究所<br>98<br>A (p,1)-total labeling of a graph G is to be an assignment of V(G)∪E(G) to integers such that: (i) any two adjacent vertices of G receive distinct integers, (ii) any two adjacent edges of G receive distinct integers, and (iii) a vertex and its incident edge receive integers that differ by at least p in absolute value. The span of a (p,1)-total labeling is the maximum difference between two labels. The minimum span of a (p,1)-total labeling of G is called to be the (p,1)-total number and denoted by λp,T(G). Let n and k be two positive integers. The graph with ver

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15

Lin, Yu-Chun, and 林育君. "On (2,1)-total labelings of generalized Petersen graphs." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/10152992644436715005.

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碩士<br>中原大學<br>應用數學研究所<br>99<br>A (p,1)- total labeling of G is an assignment of integers to V(G)∪E(G) such that any two adjacent vertices of G receive distinct integers, any two adjacent edges of G receive distinct integers, and a vertex and its incident edge receive integers that differ by at least p in absolute value. The span of a (p,1)-total labeling is the maximum difference between two labels. The minimum span of a (p,1)-total labeling of G is called the (p,1)-total number and denoted by λ^T_P(G). Let n and k be two positive integers. The graph with vertex sets {u(1),...,u(n)} and {v(

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16

CHI, FANG-CHI, and 紀芳琪. "On (2,1)-total labelings of generalized Petersen graphs." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/62589175742561935025.

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碩士<br>中原大學<br>應用數學研究所<br>99<br>A (p,1)- total labeling of G is an assignment of integers to V(G)∪E(G) such that any two adjacent vertices of G receive distinct integers, any two adjacent edges of G receive distinct integers, and a vertex and its incident edge receive integers that differ by at least p in absolute value. The span of a (p,1)-total labeling is the maximum difference between two labels. The minimum span of a (p,1)-total labeling of G is called the (p,1)-total number and denoted by λ^T_P(G). Let n and k be two positive integers. The graph with vertex sets {u(1),...,u(n)} and {v(1)

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17

Zhang, Zhe-Hao, and 張哲豪. "On (2,1)-total labelings of generalized Petersen graphs." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/79850196017786392273.

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碩士<br>中原大學<br>應用數學研究所<br>100<br>A (p,1)-total labeling of a graph G is to be an assignment of V(G)∪E(G) to integers such that any two adjacent vertices of G receive distinct integers, any two adjacent edges of G receive distinct integers and a vertex and its incident edge receive integers that differ by at least p in absolute value. The span of a (p,1)- total labeling of a graph G is the maximum difference between two labels. The minimum span of a (p,1)-total labeling of G is called the (p,1)-total number of G and denoted by λ_P^T (G). Let n and k be two positive integers. The graph with ver

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18

Choi, Yi-Cheng, and 蔡奕正. "On (a,d)-Antimagic Labeling of Generalized Petersen Graphs." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/68368123965505138023.

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碩士<br>國立交通大學<br>應用數學系所<br>98<br>In this thesis, we discuss (a,d)-antimagic labeling of generalized Petersen graph P(n,k). First, we give a necessary condition for the existence of P(n,k), and represent some previously known theorems in our setting. Then we show that P(6,2) has (12,3)-antimagic property and P(7,3) has (20,2)-antimagic by direct construction. Moreover, we show that neither P(7,2) nor P(7,3) is (7,4)-antimagic. Finally, we give a table showing (a,d)-antimagic property for P(n,k), when n=3~8; and conjecture that the same property holds for larger n.

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19

Ding, Kun-Fu, and 丁坤福. "Some Results of Incidence Coloring on Generalized Petersen Graphs and Chordal Rings." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/44656311289030408998.

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碩士<br>明志科技大學<br>工業工程與管理系碩士班<br>103<br>An incidence of G is a pair (v, e) where v ∈ V(G) is a vertex and e ∈ E(G) is an edge incident with v. Two incidences (v, e) and (w, f) are adjacent if one of the following holds: (a) v = w, (b) e = f or (c) vw = e or vw = f. Let I(G) be the set consisting of all incidences of a graph G. A proper incidence coloring of G is a mapping from I(G) to a set of colors such that adjacent incidences are assigned distinct colors. The smallest number of colors required for such a coloring is called the incidence coloring number of G, and is denoted by χi(G). In this

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