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G-designs and related designs

1993
*
Discrete Mathematics
*

.,

doi:10.1016/0012-365x(93)90408-l
fatcat:h5bupkvqnjch5h4fyckipthdnu
*G*-*designs*and related*designs*, Discrete Mathematics 116 (1993) 2999311. This is a survey*on*the existence of*G*-*designs*, bipartite*G*-*designs*and*multipartite**G*-*designs*. ... They can be solved by constructing (u, k, 1) K,-*designs*, (v, k, 1) Sk-*designs*, (m, n, k, 1)*multipartite*K,-*designs*and (m, n, k, 1)*multipartite*Sk-*designs*, respectively. ... In any case of*G*-*designs*, bipartite*G*-*designs*and*multipartite**G*-*designs*, if the*design*is*resolvable*then it is also balanced. ...##
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On the metric dimension of incidence graphs
[article]

2018
*
arXiv
*
pre-print

The metric dimension μ(Γ) is the smallest size of a

arXiv:1707.02899v2
fatcat:cvds3bpw6rdrraxkvkpqjroodm
*resolving*set for Γ. ... We consider the metric dimension of two families of incidence graphs: incidence graphs of symmetric*designs*, and incidence graphs of symmetric transversal*designs*(i.e. symmetric nets). ... In such a*design*, it follows that k = λ*g*and v = |B| = λ*g*2 , so the parameters depend only*on*λ and*g*. ...##
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Improving spatial resolution in quantum imaging beyond the Rayleigh diffraction limit using multiphoton W entangled states

2010
*
Physics Letters A
*

The

doi:10.1016/j.physleta.2010.07.068
fatcat:yrbrl2v3evcynpwtk4o3odwopm
*one*used here refers to the ability to*resolve*two point sources in the object. ... The other is the minimum angle between plane waves falling*on*an aperture that can be*resolved*and can be interpreted as*resolving*two point sources at infinity. ...##
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Anonymous secret sharing schemes

1997
*
Discrete Applied Mathematics
*

We also discuss constructions for anonymous secret sharing schemes, and apply them to access structures obtained from complete

doi:10.1016/s0166-218x(97)89208-6
fatcat:m3gannbofbe4to7wzj5kqcghdy
*multipartite*graphs. ... In this paper, we provide lower bounds*on*the size of the share sets in any (t,w) threshold scheme, and for an infinite class of non-threshold access structures. ... Let*G*=K,,,,,Wz ,_.., WI be a complete*multipartite*graph*on*k parts. If there exists a*resolvable*Steiner system S Theorem 5.3 (Stinson and Vanstone [26]). ...##
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Investigating the mitochondrial genomic landscape of Arabidopsis thaliana by long-read sequencing

2021
*
PLoS Computational Biology
*

The emergence of long-read sequencing technology is expected to yield this landscape; however, many studies aimed to assemble only

doi:10.1371/journal.pcbi.1008597
pmid:33434206
pmcid:PMC7833223
fatcat:fyagrny45ngdnmplvwmouxc3c4
*one*representative circular genome, because properly understanding*multipartite*... For synthetic data, our proposed method reliably detected*one*variation site out of 9,000-bp synthetic long reads with a 15% sequencing-error rate and produced accurate clustering. ... [0, 1] be normalized weights*on*E, and*G*0 = (V 0 , E 0 ) be the PO-HMM from*G*and w. ...##
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Index to Volume 1

1980
*
European journal of combinatorics (Print)
*

L. and FDREDI, z.,

doi:10.1016/s0195-6698(80)80042-4
fatcat:3yewjoxynfes7jzuoji6bsal6u
*On*automorphisms of line-graphs . 341 ESSER, F. and HARARY, F.,*On*the spectrum of a complete*multipartite*graph 211 FOATA, D., See ANDREWS,*G*. E. ... A., Transversal*designs*and doubly-*resolvable**designs*219 FDREDI, Z., See ERDOS, P. L. GARSIA, A. ...##
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The mitochondrial genome of Globodera ellingtonae is composed of two circles with segregated gene content and differential copy numbers

2016
*
BMC Genomics
*

We report

doi:10.1186/s12864-016-3047-x
pmid:27595608
pmcid:PMC5011991
fatcat:mkeqn2qxrnexjemzt7oslqshju
*on*the two circle*multipartite*mt genome of a newly described cyst nematode, Globodera ellingtonae. ... Results: The*G*. ellingtonae mt genome was found to be comprised of two circles, each larger than any other*multipartite*circular mt chromosome yet reported, and both were larger than the single mt circle ... All mtDNA sequence segments were covered by at least two clones, or more when needed to*resolve*discrepancies. ...##
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Page 8208 of Mathematical Reviews Vol. , Issue 99m
[page]

1999
*
Mathematical Reviews
*

*G*. Kirkpatrick [Graphs Combin. 2 (1986), no. 1, 61-66; MR 92j:05139]

*on*vertex- deleted f-factors. As an example,

*one*of the main results is as follows. Suppose

*G*has f;-factors, 1 <i < p, where °? ...

*G*. ...

##
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The Software for Constructing Trails with Local Restrictions in Graphs

2013
*
Open Journal of Discrete Mathematics
*

Let's

doi:10.4236/ojdm.2013.32017
fatcat:adcrk3uqdvgszmjrulhzf23aey
*designate*as E*G*the sets of vertices and edges of graph*G*correspondingly. ... The degree of vertex v let be*designated*as ; for let the subgraph received of graph*G*by deleting of*one*set of vertices and only all edges incident to vertices of this set.Restrictions for paths ...##
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Antipodal covers of strongly regular graphs

1998
*
Discrete Mathematics
*

Finally, antipodal covers of complete bipartite graphs and their line graphs are characterized in terms of weak

doi:10.1016/s0012-365x(97)00139-8
fatcat:shuni5ozqffhroi3psagupjgyy
*resolvable*transversal*designs*which are, in the case of maximal covering index, equivalent ... The dual of a*resolvable*transversal*design*TD(v, v/r; r) is actually a*resolvable*transversal*design*with the same parameters. ... ~ is a weak*resolvable*transversal*design*WRTD(v, r). ...##
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Assorted Musings on Dimension-critical Graphs
[article]

2021
*
arXiv
*
pre-print

Define

arXiv:2106.05333v1
fatcat:7l7uvkvgnbdlhdndupnn655t3m
*G*to be dimension-critical if every proper subgraph of*G*has dimension less than*G*. In this article, we determine exactly which complete*multipartite*graphs are dimension-critical. ... For a finite simple graph*G*, say*G*is of dimension n, and write (*G*) = n, if n is the smallest integer such that*G*can be represented as a unit-distance graph in ℝ^n. ...*Designating*by v*one*of the vertices of*G*of degree 7, we have that*G*\ {v} is isomorphic to W 6 . ...##
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Examining the Heterogeneous Genome Content of Multipartite Viruses BMV and CCMV by Native Mass Spectrometry

2016
*
Journal of the American Society for Mass Spectrometry
*

Despite their challenging size and heterogeneity, we obtained native mass spectra with

doi:10.1007/s13361-016-1348-6
pmid:26926442
pmcid:PMC4869746
fatcat:x5s5wgblaffo5bzftg5egzdqka
*resolved*series of charge states for both BMV and CCMV, demonstrating that native MS of endogenous*multipartite*virions ... However, the success rate of native MS analysis, particularly in heterogeneous mega-Dalton (MDa) protein complexes, still strongly depends*on*careful instrument modification. ... A more clearly*resolved*series of charge states is detected. Additionally, at least*one*additional poorly*resolved*series of peaks becomes visible distinct particles that were*resolved*. ...##
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A note on uniformly resolvable decompositions of K v and K v -I into 2-stars and 4-cycles

2013
*
The Australasian Journal of Combinatorics
*

In this paper we consider the uniformly

dblp:journals/ajc/Milici13
fatcat:zhmfkxctznbkxkp6l3voynmf5a
*resolvable*decomposition of the complete graph K v , or the complete graph minus a 1-factor K v − I, into two graphs such that each resolution class contains only ... A (*resolvable*) H-decomposition of the complete*multipartite*graph with u parts each of size*g*is known as a (*resolvable*) group divisible*design*H-(R)GDD of type*g*u , the parts of size*g*are called the ... When H = {K 1,2 , C 4 } a (K 1,2 , C 4 )-URGDD(r, s) of type*g*u is a uniformly*resolvable*decomposition of complete*multipartite*graph with u parts each of size*g*into r classes consisting entirely of ...##
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Page 802 of Mathematical Reviews Vol. 58, Issue 2
[page]

1979
*
Mathematical Reviews
*

Beginning with several explicit
examples, including

*one*associated with*resolvable**designs*, the author first studies partition coverings of graphs. ... Here K,, is the “star” graph of*one*vertex adjacent to b others, mG is m disjoint copies of*G*, and K, is the complete graph*on*p mutually adjacent vertices. ...##
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Resolvable 4-cycle group divisible designs with two associate classes: Part size even

2008
*
Discrete Mathematics
*

Let 1 K a denote the graph

doi:10.1016/j.disc.2006.11.043
fatcat:5yzugnduzrgvtgf4wqvdbziuzm
*on*a vertices with 1 edges between every pair of vertices. Take p copies of this graph 1 K a , and join each pair of vertices in different copies with 2 edges. ... The resulting graph is denoted by K(a, p; 1 , 2 ), a graph that was of particular interest to Bose and Shimamoto in their study of group divisible*designs*with two associate classes. ... Such decompositions are known as C z group divisible*designs*with two associate classes, following the notation of Bose and Shimamoto who considered the existence problem for K z group divisible*designs*...
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