Relevant bibliographies by topics / Petersen graph

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Petersen graph'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Petersen graph"

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P, Sumathi, and Suresh Kumar J. "Fuzzy Quotient -3 Cordial Labeling on Generalized Petersen Graph." Indian Journal of Science and Technology 16, no. 9 (2023): 648–59. https://doi.org/10.17485/IJST/v16i9.1720.

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Abstract <strong>Objectives:</strong>&nbsp;To analyze the existence of fuzzy quotient-3 cordial labeling on the generalized Petersen graph.&nbsp;<strong>Methods:</strong>&nbsp;The method involves mathematically defining how to label the vertex of a generalized Petersen graph and demonstrating that these formulations produce fuzzy quotient-3 cordial labeling.&nbsp;<strong>Findings:</strong>&nbsp;In this study, we proved that the generalized Petersen graph GP(h;m) ; 1 m &lt; &lfloor; h 2 &rfloor; is fuzzy quotient-3 cordial, except for h 0( mod 6).&nbsp;<strong>Novelty:</strong>&nbsp;Here, we gi
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Ahmad, Mukhtar, Saddam Hussain, Ulfat Parveen, Iqra Zahid, Muhammad Sultan, and Ather Qayyum. "On Degree-Based Topological Indices of Petersen Subdivision Graph." European Journal of Mathematical Analysis 3 (June 5, 2023): 20. http://dx.doi.org/10.28924/ada/ma.3.20.

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In this paper, we adequately describe the generalised petersen graph, expanding to the categories of graphs. We created a petersen graph, which is cyclic and has vertices that are arranged in the centre and nine gons plus one vertex, leading to the factorization of regular graphs. Petersen graph is still shown in graph theory literature, nevertheless.
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Lv, Shengmei, and Liying Zhao. "Hamiltonian Indices of Three Classes of Graphs Obtained from Petersen Graph." Axioms 12, no. 6 (2023): 580. http://dx.doi.org/10.3390/axioms12060580.

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In this paper, we mainly consider the Hamiltonian indices of three classes of graphs obtained from Petersen graph, that is, the minimum integer m of m-time iterated line graph Lm(G) of these three classes of graphs such that Lm(G) is Hamiltonian. We show that the Hamiltonian indices of those graphs obtained by replacing every vertex of Petersen graph with a n-cycle or a complete graph of order n, or adding n pendant edges to each vertex of Petersen graph are both 2. In addition, we also study the situations of adding an edge to these three classes of graphs and obtain that their Hamiltonian in
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Beaula, C., та P. Venugopal. "Cryptosystem Using the Generalized Petersen Graph 𝐺𝑃 (𝟐𝑛 + 𝟏, 𝟐)". Indian Journal Of Science And Technology 17, № 30 (2024): 3125–37. http://dx.doi.org/10.17485/ijst/v17i30.1130.

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Objective: In the digital era, data transfer in a network without external interference is one of the challenging problems. External interference can be minimized by creating a strong cryptosystem. For this purpose, different mathematical concepts are incorporated to construct a cryptosystem. Recently, techniques in graph theory, a branch of mathematics, are also employed in cryptography. The objective of this paper is to propose a new cryptosystem to encrypt and decrypt an alphabetical string of lengths less than equal to 16 using graph decomposition and edge labeling on a generalized Peterse
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C, Beaula, та Venugopal P. "Cryptosystem Using the Generalized Petersen Graph 𝐺𝑃 (𝟐𝑛 + 𝟏, 𝟐)". Indian Journal of Science and Technology 17, № 30 (2024): 3125–37. https://doi.org/10.17485/IJST/v17i30.1130.

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Abstract <strong>Objective:</strong>&nbsp;In the digital era, data transfer in a network without external interference is one of the challenging problems. External interference can be minimized by creating a strong cryptosystem. For this purpose, different mathematical concepts are incorporated to construct a cryptosystem. Recently, techniques in graph theory, a branch of mathematics, are also employed in cryptography. The objective of this paper is to propose a new cryptosystem to encrypt and decrypt an alphabetical string of lengths less than equal to 16 using graph decomposition and edge la
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Li, Xiao Min, Lan Lei, Hong-Jian Lai, and Meng Zhang. "Supereulerian graphs and the Petersen graph." Acta Mathematica Sinica, English Series 30, no. 2 (2014): 291–304. http://dx.doi.org/10.1007/s10114-014-2272-y.

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Catlin, Paul A., and Hong-Jian Lai. "Supereulerian Graphs and the Petersen Graph." Journal of Combinatorial Theory, Series B 66, no. 1 (1996): 123–39. http://dx.doi.org/10.1006/jctb.1996.0009.

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Bednarz, Paweł, and Natalia Paja. "On (2-d)-Kernels in Two Generalizations of the Petersen Graph." Symmetry 13, no. 10 (2021): 1948. http://dx.doi.org/10.3390/sym13101948.

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A subset J is a (2-d)-kernel of a graph if J is independent and 2-dominating simultaneously. In this paper, we consider two different generalizations of the Petersen graph and we give complete characterizations of these graphs which have (2-d)-kernel. Moreover, we determine the number of (2-d)-kernels of these graphs as well as their lower and upper kernel number. The property that each of the considered generalizations of the Petersen graph has a symmetric structure is useful in finding (2-d)-kernels in these graphs.
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R, Suguna. "Characteristics of Fuzzy Petersen Graph and Platonic Graph with Fuzzy Rule." International Journal for Research in Applied Science and Engineering Technology 10, no. 2 (2022): 374–78. http://dx.doi.org/10.22214/ijraset.2022.40273.

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Abstract: Graph theory is the concepts used to study and model various application in different areas. In this paper, we consider the The Petersen and also the Platonic graph using if-then-rules fuzzy numbers. The results are related to the find the degree of odd vertices and even verticesare same by applying if-then-rules through the paths described by fuzzy numbers. Keywords: Degree of Vetex, Incident Graph, Peterson Graph, Platonic graph, Fuzzy IF-THEN rule.
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B.Jothilakshmi. "Degree-Based Topological Indices of Modified Petersen Graph." Panamerican Mathematical Journal 35, no. 4s (2025): 235–46. https://doi.org/10.52783/pmj.v35.i4s.4673.

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Objectives:The Petersen graph is non-planar, meaning it cannot be drawn on a plane without edge crossings. This limits its use in applications requiring planar graphs, such as circuit board design, geographic mapping, or any domain where planar embeddings are essential. The Petersen graph is fixed with only 10 vertices and 15 edges. Its small size can make it unsuitable for modelling or analysing larger, more complex systems. The weakness of unsuitable for modelling or analysing larger, more complex systems estimation is the lack of consideration of the graph and it is not a function of the ov
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Dissertations / Theses on the topic "Petersen graph"

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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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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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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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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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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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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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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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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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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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Books on the topic "Petersen graph"

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Holton, Derek. The Petersen graph. Cambridge University Press, 1993.

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J, Sheehan, ed. The Petersen graph. Cambridge University Press, 1993.

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Sheehan, J., and D. A. Holton. Petersen Graph. Cambridge University Press, 2011.

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Sheehan, J., and D. A. Holton. Petersen Graph. Cambridge University Press, 2010.

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Andersen, L. D., J. Bang-Jensen, T. R. Jensen, L. K. Jørgensen, and G. Sabidussi. Julius Petersen Graph Theory Centennial. Elsevier Science & Technology Books, 2016.

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The Julius Petersen graph theory centennial. North-Holland, 1992.

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Petersen, Elfriede. Graph Paper Composition Notebook: Hat and Glasses Graph Paper Composition, Grid Paper Notebook, Quad Ruled, 100 Sheets, Size 8. 5 X 11 by Elfriede Petersen. Independently Published, 2021.

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Book chapters on the topic "Petersen graph"

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Geyer-Schulz, Andreas, and Fabian Ball. "Comparing Partitions of the Petersen Graph." In Advanced Studies in Behaviormetrics and Data Science. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2700-5_5.

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Rela, Guillermo, Franco Robledo, and Pablo Romero. "Petersen Graph is Uniformly Most-Reliable." In Lecture Notes in Computer Science. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-72926-8_35.

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Chia, G. L., and C. L. Lee. "Crossing Numbers and Skewness of Some Generalized Petersen Graphs." In Combinatorial Geometry and Graph Theory. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-30540-8_8.

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Bezrukov, Sergei L., Sajal K. Das, and Robert Elsässer. "Optimal Cuts for Powers of the Petersen Graph." In Graph-Theoretic Concepts in Computer Science. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46784-x_23.

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Öhring, Sabine R., and Sajal K. Das. "The folded Petersen network: A new versatile multiprocessor interconnection topology." In Graph-Theoretic Concepts in Computer Science. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-57899-4_61.

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Das, Angsuman. "Determining Number of Generalized and Double Generalized Petersen Graph." In Algorithms and Discrete Applied Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39219-2_11.

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Debnath, Chinmay, and Alak Kumar Datta. "A Short Note on Spanning Cactus Problem of Petersen Graph." In Learning and Analytics in Intelligent Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42363-6_88.

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Kartheek, Mukku Nisanth, Munaga V. N. K. Prasad, and Raju Bhukya. "Petersen Graph Based Binary Pattern for Person Independent Facial Expression Recognition." In Lecture Notes in Computer Science. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-12700-7_44.

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Banu Priya, S., and A. Parthiban. "Equitable Power Domination Number of Generalized Petersen Graph, Balanced Binary Tree, and Subdivision of Certain Graphs." In Springer Proceedings in Mathematics & Statistics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4646-8_16.

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Gu, Xiaofeng, and William Zhang. "Cyclically Orderable Generalized Petersen Graphs." In Algorithmic Aspects in Information and Management. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16081-3_26.

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Conference papers on the topic "Petersen graph"

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Xu, Jie. "Enhanced Local Face Feature Encoding via the Petersen Graph Framework." In 2024 5th International Conference on Computer Engineering and Intelligent Control (ICCEIC). IEEE, 2024. https://doi.org/10.1109/icceic64099.2024.10775666.

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Xie, Fang, and Yanzhong Hu. "Research on the Nonplanarity of the Petersen Graph." In 2010 2nd International Symposium on Information Engineering and Electronic Commerce (IEEC). IEEE, 2010. http://dx.doi.org/10.1109/ieec.2010.5533254.

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Susilowati, Liliek, Izza Wardatul Mufidah, and Nenik Estuningsih. "The dominant metric dimension of generalized Petersen graph." In 4TH INTERNATIONAL SCIENTIFIC CONFERENCE OF ALKAFEEL UNIVERSITY (ISCKU 2022). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0181076.

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Klobas, Nina, and Matjaž Krnc. "Fast Recognition of Some Parametric Graph Families." In 7th Student Computer Science Research Conference. University of Maribor Press, 2021. http://dx.doi.org/10.18690/978-961-286-516-0.7.

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Recognizing graphs with high level of symmetries is hard in general, and usually requires additional structural understanding. In this paper we study a particular graph parameter and motivate its usage by devising eÿcient recognition algorithm for the family of I-graphs. For integers m a simple graph is cycle regular if every path of length ` belongs to exactly cycles of length m. We identify all cycle regular I-graphs and, as a conse-quence, describe linear recognition algorithm for the observed family. Similar procedure can be used to devise the recog-nition algorithms for Double generalized
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Tan Xuegong. "The forwarding index and diagnosability of folded Petersen graph." In 2010 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE 2010). IEEE, 2010. http://dx.doi.org/10.1109/icacte.2010.5579613.

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Mednykh, Ilya Alexandrovich, and Lilia Alexandrovna Grunvald. "Number of labelled spanning forests for circulant foliation over graph." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-60.

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This report will present a new method for obtaining exact formulas for the number of marked spanning forests f(n) for an infinite family graphs H&lt;sub&gt;n&lt;/sub&gt; = H&lt;sub&gt;n&lt;/sub&gt;(G&lt;sub&gt;1&lt;/sub&gt;, G&lt;sub&gt;2&lt;/sub&gt;,...,G&lt;sub&gt;m&lt;/sub&gt;) obtained as a circulant foliation over graph H with m vertices and fibers G&lt;sub&gt;1&lt;/sub&gt;, G&lt;sub&gt;2&lt;/sub&gt;,...,G&lt;sub&gt;m&lt;/sub&gt;. Each such layer in turn, is a circulant graph with n vertices. Given the family includes generalized Petersen graphs, I-graphs, sandwiches of circulant graphs,
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Hu, Yanzhong. "Notice of Retraction: New Proof of Some Properties about Petersen Graph." In 2010 2nd International Workshop on Education Technology and Computer Science (ETCS). IEEE, 2010. http://dx.doi.org/10.1109/etcs.2010.145.

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Tan, Yi-Hong, Xi-Dao Luan, Ya-Ping Lin, and Zhao Bi-hai. "DLPSPN: New Efficient Super-Peer Network Based on Double-Loop Petersen Graph." In 2011 International Conference on Network Computing and Information Security (NCIS). IEEE, 2011. http://dx.doi.org/10.1109/ncis.2011.138.

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Kavitha, B., and C. Vimala. "An algorithmic approach to edge - Odd graceful labeling of generalized Petersen graph using advanced python programming." In INNOVATIONS IN THERMAL, MANUFACTURING, STRUCTURAL AND ENVIRONMENTAL ENGINEERING: ICITMSEE’24. AIP Publishing, 2025. https://doi.org/10.1063/5.0273016.

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Faria, Luerbio, Mauro Nigro, and Diana Sasaki. "Total coloring line graphs of generalized Petersen graphs." In v. 11 n. 1 (2025): CNMAC 2024. SBMAC, 2025. https://doi.org/10.5540/03.2025.011.01.0490.

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