groups cayley graphs and rips complexes

... of perfect graphs Let An , Bn be the adjacency graphs of the graph Gn and the digraph Γn respectively ⊤ We then have An = Bn = Bn if and only if −1 is a quadratic residue modulo n, and ⊤ ⊤ An ... √ n Maistrelli and Penman [13] use this to show that the Payley graphs of prime ω(G) order are not perfect.2 Noting that odd-order Paley graphs are also quadratic unitary Cayley graphs, we may ... we noted in the introduction and in Section 3.5, the graphs Gn for n ≡ (mod 4) prime are also Paley graphs Shparlinski [17] shows that prime-order Paley graphs these graphs have high energy (i.e...

Ngày tải lên: 08/08/2014, 12:22

... developed by Renteln[3] and Ku and Wong[8] to determine the eigenvalues of this graph By investigating property of power sum symmetric function, we derive some new Cayley graphs and determine their ... able to produce new graphs and calculate their eigenvalues We also look at some subgraphs of derangement graph and generalize properties in derangement graph into these subgraphs by analysis of ... graph, developed by Ku and Wong[8] By studying the usage of power sum symmetric function, we thus develop some new Cayley graphs and determine some of their eigenvalues and other properties This...

Ngày tải lên: 03/10/2015, 11:36

... except for G = Z4 and Γ = K4 , or G = Z6 and Γ = K3,3 or G = Z6 and Γ = K6 or G = Z10 and Γ = K5,5 Our work is entirely dependent on two papers [1] and [3] that classify the graphs Γ as in the ... 2001 B D McKay and C E Praeger, Vertex transitive graphs which are not Cayley graphs I , J Austral, Math, Soc Ser A 56 (1994) 53–63 C E Praeger, Finite Normal Edge-Transitive Cayley Graphs, Bull ... Tavallaee, and Ali A Talebi Proposition 2.2 [2] A graph Γ = (V, E) is a Cayley graph of a group if and only if AutΓ contains a regular subgroup Let Γ = Cay(G, S) be a Cayley graph of G on S, and let...

Ngày tải lên: 06/08/2014, 05:20

... 147 (1993) 441454 [19] P R Hafner, Large Cayley graphs and digraphs with small degree and diameter, Computational Algebra and Number Theory (W Bosma and van der Poorten, Eds.) Kluwer, Amsterdam ... paper is to show that, in fact, all the Cayley graphs of semidirect products of groups which appear in the tables of largest known graphs of given degree and diameter [11, 19, 10] can be described ... parallel edges, loops, and semiedges in our Cayley graphs Whenever xi = xj for some i = j, from each vertex b we have a pair of parallel arcs (b, i) and (b, j) If xi = id and i = τ (i), we have...

Ngày tải lên: 07/08/2014, 06:22

... classical result that the cyclic graphs C3 , C4 , and C5 require three labels but that the other cyclic graphs only need two In other words, either two or three handles are needed to tell keys ... vertex orbits This highlights the main algebraic difference between distinguishing groups and distinguishing graphs: many groups not act faithfully while the automorphism group of a graph always has ... φO and φX\O Consequently g is in the subgroup Stab(O) ∩ Stab(X\O) and so g is in Stab(X) This gives a numerical condition for 2-distinguishability Corollary 2.4 Suppose Γ acts on X and O1 and...

Ngày tải lên: 07/08/2014, 08:20

... vertices This implies that the only graphs which have fix(G) = n − are the complete graphs and the empty graphs On the other hand, the graphs with fix(G) = are the rigid graphs [1], which have trivial ... k, and fix(Γ) = {1, , k} 3.2 Symmetric groups The inflation of a graph G, Inf(G), is a graph with a vertex for each ordered pair (v, e), where v and e are a vertex and an edge of G, and v and ... uk+1) and v = (v1 , , vk+1) are adjacent if and only if there exists some index i such that uj = vj for all j < i, ui = vi , and uj = vi and vj = ui for all j > i Lemma 15 The graphs Gk and Inf...

Ngày tải lên: 07/08/2014, 21:21

... normal subgroup which is regular and isomorphic to G, then Γ is called a normal Cayley graph of G Locally primitive Cayley graphs and 2-arc-transitive Cayley graphs have been extensively studied, ... primitive normal Cayley graphs of metacyclic groups are in these constructions Theorem 1.3 Graphs in Constructions 4.1 − 4.3 are exactly form the class of locally primitive normal Cayley graphs of metacyclic ... Li, Finite edge-transitive Cayley graphs and rotary Cayley maps, Trans Amer Math Soc 358 (2006), 4605-4635 [9] C H Li, J Pan, Finite 2-arc-transitive abelian Cayley graphs, Europ J Combin 29(2007),...

Ngày tải lên: 08/08/2014, 01:20

... All Hamming graphs are proven to be integral Cayley graphs, which extends a partial result in [14] Moreover, we show that certain graphs associated with the Sudoku puzzle and with pandiagonal ... [1] Abdollahi, A., and Vatandoost, E Which Cayley graphs are integral? Electronic J Comb 16(1) (2009), R122, 1–17 [2] Ahmadi, O., Alon, N., Blake, L F., and Shparlinski, I E Graphs with integral ... Lov´sz [12] that all Cayley graphs over Z2 (“cubelike graphs ) are integral The following a theorem extends this result Theorem 13 All nontrivial abelian Cayley integral groups are represented...

Ngày tải lên: 08/08/2014, 12:22

... integral Cayley graphs with 10 vertices Lemma 2.23 There are exactly three connected, integral Cayley graphs with nine vertices Proof We show that the graphs Γ19 , Γ21 and Γ24 are Cayley graphs and ... There are exactly five connected, integral Cayley graphs with ten vertices Proof We show that the graphs Γ26 , Γ27 , Γ35 , Γ36 and Γ37 are Cayley graphs and others are not (See table 4) By table ... By Theorem 2.11, the graphs Γ38 , Γ39 and Γ40 are not Cayley graphs It is clear that if G is a finite group of order 10 and |S| = 9, then Γ(S : G) is the complete graph K10 and so Γ(S : G) = Γ26...

Ngày tải lên: 08/08/2014, 14:23

... tonnes.Bangladesh,Viet Nam and Thailand had similar leuelsofproduction, i.e between20 and 30 million tonneseach, while Malaysia, Japan and the Philippines ranged between16 and l0 million tonne* The ... meat excePt that in 1950 production ofpoulny and sheepand goat meat d) The graplt shouts was less than million tons, uthileproduction ofpork and beefand buffalo uas around 20 million tons 1n€At ... productionincreased Pouhry and rose dramatically steady Beefand bffilo productionexperienced grouth a Answer Ke! of 2.3 Expressions Measurement it for Since graphs and tablesshow measurements,...

Ngày tải lên: 25/10/2013, 07:20

... Exam Areas Graphs Information may be displayed in many ways The three basic types of graphs you should know are bar graphs, line graphs, and pie graphs (or pie charts) Bar Graphs Bar graphs convert ... Delegates Committed to Each Candidate Candidate Candidate Candidate Candidate 200 400 600 800 Delegates Candidate has approximately how many more delegates committed than does Candidate 2? A 150 B 200 ... two years was the greatest rise in average test scores? A 1978 and 1979 B 1979 and 1980 C 1980 and 1981 D 1981 and 1982 E 1982 and 1983 E The most efficient way to compute greatest rise is to...

Ngày tải lên: 01/11/2013, 14:20

... any two elements x and y of L have a greatest lower bound, called the infimum of x and y and denoted by inf(x, y), anda smallest greater bound, called the supremum of x and y and denoted by sup(x, ... M.A Kiwi, “Games on line graphes and sand piles”, Theoret Comput Sci., 115 (1993) 321 [7] E Goles, M Latapy, C Magnien, M Morvan, H.D Phan, “Sandpile models and lattices: a comprehensive survey”, ... em So by using Theorem 1, we have g ≥ c and g ≥ d On the other hand, let h be a configuration of CCFG(T,n) satisfying h ≥ c,d We have eV(i, h) ≤ eV(i, c) and eV(i, h) ≤ eV(i, d) for all nodes i...

Ngày tải lên: 12/02/2014, 17:20

... E53QbsSHMT and its binary complexes with Gly, l-Ser, l-allo-Thr and ternary complex with Gly and 5-formyl-THF (FTHF) In addition, the biochemical and spectral properties of these complexes were ... Gly and Ser external aldimine complexes of E75Q and E75LrcSHMT, the electron density for the ligands was not well defined [15] In contrast, excellent electron density was observed for the ligands ... [12] Both bsSHMT and E53QbsSHMT ternary complexes were dialyzed against buffer (50 mm potassium phosphate pH 7.4 containing mm EDTA and mm 2-mercaptoethanol) devoid of Gly and FTHF and spectra were...

Ngày tải lên: 18/02/2014, 16:20

... W3A1, 1O96 [3] a- and b-ETF chains are shown as magenta and blue cartoons FAD and AMP are shown as yellow and orange sticks, respectively Conserved Leub195 ⁄ 194 for human and W3A1 ETFs, respectively, ... domains II and III in human (A) and Methylophilus methylotrophus W3A1 (B) ETFs PDB codes: human, 1EFV [1]; W3A1, 1O96 [3] a- and b-ETF chains are shown as magenta and blue cartoons and sticks ... dimer of MCAD and ETF are shown for clarity PDB code for all, 2A1T [25] a- and b-ETF chains and MCAD are shown as magenta, blue and green cartoons, respectively The cofactors FAD and AMP are shown...

Ngày tải lên: 07/03/2014, 05:20

... program as amino acid sequences Amino acid residues, N- and C-terminal end groups, and modifications can be custom defined, including specific isotopic and ⁄ or virtual labelling to keep track of specific ... predict and optimize possible outcomes beforehand, which saves time in finding successful experimental strategies asap and searchxlinks [11] have the order of events hard coded into the program and ... Netherlands Organization for Scientific Research (NWO), Chemical Sciences division (CW) and Regieorgaan Genomics The ApexQ FTICR-mass spectrometer was largely funded by NWO-CW and the TofSpec 2EC and...

Ngày tải lên: 07/03/2014, 12:20

... and P3/P3¢ ligands, the S3/S3¢ sites can be reached by substituents on the P1/P1¢ ligands To test this, compounds 7–9 were synthesized Compounds and are substituted with thienly and pyridyl groups ... loops The side chain of ˚ ˚ Asp30 and Val32 moves as much as 2.0 A and 0.6 A, respectively, to accommodate the benzyl and 2-chloro-6fluorobenzyl groups of compounds and (Fig 4) Fig shows a summary ... donation of hydrogens via the main-chain amide groups These two compounds and represent the two groups of inhibitors in this study Compound (A) has 10 and compound (B) has hydrogenbond donors/acceptors...

Ngày tải lên: 08/03/2014, 02:20

... readily understandable way Software tools for handling graphs are also required Formal features of graphs can express the underlying characteristics of articles More efficient and useful algorithms ... Applications in Knowledge Navigation and Retrieval N Jardine, and R Sibson 1968 The Construction of Hierarchic and Non-Hierarchic Classifications Computer, pages 177-184 I Mani and E Bloedorn 1997 Multi-document ... graphs We are now evaluating our method by testing it with various strategies The development of a technique for visualizing directed graphs is another task for the future Although directed graphs...

Ngày tải lên: 08/03/2014, 06:20

... equals sign and then continue typing the formula Rather than typing this in the remaining nine cells, B2-B10, we can highlight B1 through B10, then click EDIT on the toolbar, and select FILL and DOWN ... scientific notation from this screen Also under FORMAT, then CELLS you can change the font and colors of both the font and background You should be able to use these features It is possible to perform ... ‘display equation on chart’ and ‘display R-squared value on chart.’ As you can see, the data points not fall exactly on the line We need to know the error in the slope and intercept of the trendline,...

Ngày tải lên: 14/03/2014, 18:33

... paclitaxel resistance and IDN5390 sensitivity, through the analysis of the complexes between these two ligands and the isotypes I and III of the human b-tubulin We also investigated the complexes involving ... between the M-loop and helix H7, interacting with them essentially through: (i) hydrogen bonds involving C3 and C7 hydroxyl groups and lateral chains of Arg278 and Gln282, respectively; and (ii) p–p ... ring and His229 In E3, the ligand is farther away from the M-loop and shifted towards helix H1 and the S9–S10 loop with respect to the E1 complex, and therefore is Table Free energy, enthalpy and...

Ngày tải lên: 16/03/2014, 13:20

... mentor and colleague in philosophy and mathematics, J S Song and his JJFS; my brother and companion in wine and Existentialism, N Moeller and his Marina To my collaborators: my colleagues and brethren, ... I am, to have my dear mother and father, my aunt DaYi and grandmother, embrace me with fourtimes compounded love! Every fault, a tear, every wrong, a guiding hand and every triumph, an exaltation ... Theory and Yang-Mills in Graph Theory 179 12.5 Concluding Remarks and Prospects 185 13 Orbifolds IV: Finite Groups and WZW Modular Invariants, Case Studies for SU(2) and...

Ngày tải lên: 17/03/2014, 14:50