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On the P_3-hull number and infecting times of generalized Petersen graphs
[article]
2022
arXiv
pre-print
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In this paper, we study the P_3-hull number for generalized Petersen graphs and a number of closely related graphs that arise from surgery or more generalized permutations. ...
In addition, the number of components of the complement of an infecting set of minimum cardinality is calculated for the generalized Petersen graph and shown to always be 1 or 2. ...
Statements and Declarations The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. ...
arXiv:2201.00078v2
fatcat:ladmwztc7fbsbnbuadss3cxcyu
Cycle Intersection Graphs and Minimum Decycling Sets of Even Graphs
[article]
2018
arXiv
pre-print
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Links between the cycle rank of the cycle intersection graph of an even graph and the decycling number of the even graph itself are found. ...
We introduce the cycle intersection graph of a graph, an adaptation of the cycle graph of a graph, and use the structure of these graphs to prove an upper bound for the decycling number of all even graphs ...
the exact decycling number of the (generalized) Petersen graph [8] . ...
arXiv:1810.04252v1
fatcat:ycolcehlxzehvdpkttggntinmy
Acyclic sum-list-colouring of grids and other classes of graphs
2017
Opuscula Mathematica
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Especially, we give the exact value of the D1-sum-choice-number for each grid Pn Pm, when at least one of the numbers n, m is less than five, and for each generalized Petersen graph. ...
Moreover, we present some results that estimate the D1-sum-choice-number of an arbitrary graph in terms of the decycling number, other graph invariants and special subgraphs. ...
As a consequence we conclude the exact values of the D 1 -sum-choice-numbers of all graphs G for which ∆(G) ≤ 3, including all generalized Petersen graphs (Corollaries 4.1, 4.2). ...
doi:10.7494/opmath.2017.37.4.535
fatcat:navmml4mmfhfnhjxu6li2bzewq
Decycling Number of Linear Graphs of Trees
[article]
2018
arXiv
pre-print
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We also give bounds on the decycling number of line graph of k-ary trees and determine the exact the decycling number of line graphs of perfect k-ary trees. ...
The decycling number of a graph G is the minimum number of vertices whose removal from G results in an acyclic subgraph. ...
Bounds on the decycling numbers have been established for some well-known graphs, such as hypercubes [4] , star graphs [12] , generalized petersen graphs [7] , distance graphs and circulant graphs ...
arXiv:1701.01953v3
fatcat:e5tbwuhfwjbh7crlyyom6ysgku
Feedback Arc Number and Feedback Vertex Number of Cartesian Product of Directed Cycles
2019
Discrete Dynamics in Nature and Society
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For a digraph D, the feedback vertex number τD, (resp. the feedback arc number τ′D) is the minimum number of vertices, (resp. arcs) whose removal leaves the resultant digraph free of directed cycles. ...
In this note, we determine τD and τ′D for the Cartesian product of directed cycles D=Cn1→□Cn2→□...Cnk→. Actually, it is shown that τ′D=n1n2...nk∑i=1k1/ni, and if nk≥...≥n1≥3 then τD=n2...nk. ...
Acknowledgments Research supported by NSFC (No. 11571294) , the Key Laboratory Project of Xinjiang (2018D04017). e authors are grateful to the referees for their helpful suggestions. ...
doi:10.1155/2019/7028573
fatcat:agautkqqo5bnnd773ehytn66um
Matching Preclusion of the Generalized Petersen Graph
2019
Theory and Applications of Graphs
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In this paper we determine the matching preclusion number for the generalized Petersen graph P (n, k) and classify the optimal sets. ...
The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph with no perfect matchings. ...
The properties of the generalized Petersen graphs have been widely studied regarding perfect 2-colorings, the decycling number, and domination number [2, 13, 15] . ...
doi:10.20429/tag.2019.060105
fatcat:vm5nafobsjgnfmcyashofifkou
The strong metric dimension of some generalized Petersen graphs
2017
Applicable Analysis and Discrete Mathematics
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In this paper the strong metric dimension of generalized Petersen graphs GP(n,2) is considered. ...
The exact value is determined for cases n=4k and n=4k+2, while for n=4k+1 an upper bound of the strong metric dimension is presented. ...
ACKNOWLEDGEMENT This research was partially supported by Serbian Ministry of Education, Science and Technological Development under the grants no. 174010 and 174033. ...
doi:10.2298/aadm161110032k
fatcat:oapvxr5f3jgbta25zlryh5nwmq
Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs
2020
Revista de la Unión Matemática Argentina
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We consider the weakly convex and convex domination numbers for two classes of graphs: generalized Petersen graphs and flower snark graphs. ...
For a given generalized Petersen graph GP (n, k), we prove that if k = 1 and n ≥ 4 then both the weakly convex domination number γwcon(GP (n, k)) and the convex domination number γcon(GP (n, k)) are equal ...
Conclusions In this paper, the weakly convex domination number and convex domination number for the generalized Petersen graphs and flower snark graphs are studied. ...
doi:10.33044/revuma.v61n2a16
fatcat:v7rqeoxpsrf47myx2w5l3yi52e
The k-conversion number of regular graphs
[article]
2018
arXiv
pre-print
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The k-conversion number c_k(G) is the size of a minimum k-conversion set of G. A set X⊆ V is a decycling set, or feedback vertex set, if and only if G[V-X] is acyclic. ...
We present classes of cubic graphs that attain the bound for c_2(G), and others that exceed it---for example, we construct classes of 3-connected cubic graphs H_m of arbitrary girth that exceed the lower ...
This generalized the lower bound obtained by Staton [32] on the decycling number of (k + 1)-regular graphs, which corresponds to the k-conversion number. ...
arXiv:1812.03250v1
fatcat:rrswkalnfbfnhpzxovzyldnefq
Girth, oddness, and colouring defect of snarks
[article]
2022
arXiv
pre-print
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The colouring defect of a cubic graph, introduced by Steffen in 2015, is the minimum number of edges that are left uncovered by any set of three perfect matchings. ...
Our aim is to examine the relationship of colouring defect to oddness, an extensively studied measure of uncolourability of cubic graphs, defined as the smallest number of odd circuits in a 2-factor. ...
The first and the third author were partially supported by the grant VEGA 2/0078/20 of Slovak Ministry of Education. ...
arXiv:2106.12205v3
fatcat:yod7bzzwafhp7gs4ykn34446xu
Acyclic polynomials of graphs
[article]
2022
arXiv
pre-print
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For each nonnegative integer i, let a_i be the number of i-subsets of V(G) that induce an acyclic subgraph of a given graph G. ...
We define A(G,x) = ∑_i ≥ 0 a_i x^i (the generating function for a_i) to be the acyclic polynomial for G. ...
. ✷ Since it is, in general, NP-hard to determine the decycling number ∇(G) of a graph G, it is likewise intractable to determine the acyclic polynomial A(G, x) for a general graph. ...
arXiv:2011.01735v3
fatcat:dx3h5hkymfc27ck43c33bkp7ji
Feedback Numbers of Goldberg Snark, Twisted Goldberg Snarks and Related Graphs
2019
ITM Web of Conferences
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Let f(n) denote the feedback numbers of these graphs, we prove that f(n)=2n+1, for n≥3. ...
In this paper, we determine the exact values of the feedback numbers of the Goldberg snarks Gn and its related graphs Gn * , Twisted Goldberg Snarks TGn and its related graphs TGn * . ...
The minimum cardinality of a feedback vertex set is called the feedback number (or decycling number proposed first by Beineke and Vandell [1] ) of G. ...
doi:10.1051/itmconf/20192501012
fatcat:fvj2eeovi5h6boiqwafbv3w7am
Target set selection problem for honeycomb networks
[article]
2012
arXiv
pre-print
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set for different kinds regular graphs in the class of honeycomb networks ...
Let G be a graph with a threshold function θ:V(G)→N such that 1≤θ(v)≤ d_G(v) for every vertex v of G, where d_G(v) is the degree of v in G. Suppose we are given a target set S⊆ V(G). ...
The size of a minimum feedback vertex set in a graph G is called the decycling number of G and is denoted by ∇(G) (adapted from [29] ). ...
arXiv:1203.0666v1
fatcat:3t2475ml3fceph3ie6p6a7xlvm
On the $P_3$-hull number and infecting times of generalized Petersen graphs
[article]
2022
Preserved Fulltext
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In this paper, we study the $P_3$-hull number for Petersen graphs and a number of closely related graphs that arise from surgery or more generalized permutations. ...
In addition, the number of components of the complement of a minimal infecting set is calculated for the Petersen graph and shown to always be $1$ or $2$. ...
Statements and Declarations The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. ...
doi:10.48550/arxiv.2201.00078
fatcat:lrvhcw6pefdpreb5n6pcotaywq
Hepatic Oxidative Stress, Genotoxicity and Vascular Dysfunction in Lean or Obese Zucker Rats
2015
PLoS ONE
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Collectively, the results indicate that obese Zucker rats only displayed a modest mesenteric vascular dysfunction, with no increase in hepatic oxidative stress-generated DNA damage despite substantial ...
The 37 week old lean rats also had higher expression level of Hmox1 and elevated levels of DNA strand breaks in the liver. ...
Acknowledgments The authors are also thankful to Rasmus Koefoed Petersen and Hanne Vie at The August Krogh Centre for their assistance with the visualisation of HMOX-1 protein.
Author Contributions ...
doi:10.1371/journal.pone.0118773
pmid:25738756
pmcid:PMC4349582
fatcat:ddbikfsdd5bxvg3jjxpz5qh2tm
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