Download A First Course in Graph Theory and Combinatorics by Sebastian M. Cioaba, M. Ram Murty PDF

By Sebastian M. Cioaba, M. Ram Murty

The concept that of a graph is key in arithmetic because it with ease encodes assorted relatives and enables combinatorial research of many complex counting difficulties. during this ebook, the authors have traced the origins of graph idea from its humble beginnings of leisure arithmetic to its glossy surroundings for modeling conversation networks as is evidenced via the realm huge net graph utilized by many net se's. This e-book is an advent to graph thought and combinatorial research. it truly is according to classes given through the second one writer at Queen's collage at Kingston, Ontario, Canada among 2002 and 2008. The classes have been aimed toward scholars of their ultimate yr in their undergraduate program.

Errate: http://www.math.udel.edu/~cioaba/book_errata.pdf

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TAG " & & substr ( seq ,j , j +2) ! = " TGA " ) { j <- j + 3 } © 2009 by Taylor & Francis Group, LLC Introduction 17 if ( j +2 <= nchar ( seq ) ) { if ( j +2 - i +1 > jj +2 - ii +1) { ii <- i jj <- j } } } i <- i + 3 } } c ( ii , jj +2) } The longest of the 104 open reading frames with at least 30 nucleotides in the DNA sequence of Bacteriophage φ-X174 has indeed 2,284 − 1,001 + 1 = 1,284 nucleotides. > longest . open . reading . frame ( seq ) [1] 1001 2284 The actual reading frame it belongs to can be obtained by integer division.

AABAAABBAAAABBB A B BA A B BB A A A BB B B AA A A B B B B B The corresponding labeled sequences, of length 15 and 24, are as follows. (A ,9) (B ,6) (A ,10) (B ,14) Their symmetric difference is thus the following labeled sequence, of length 9. 1 Traversing Labeled Sequences Most algorithms on sequences require a systematic method of accessing the elements of a sequence, and combinatorial pattern matching algorithms are no exception. The most common method for accessing the elements of a sequence is by traversing the ordered list of elements, from first to last.

Function alignment free distance(S1 , S2 , k, Σ) F1 ← word composition(S1 , k, Σ) F2 ← word composition(S2 , k, Σ) cov ← covariance(F1 , F2 ) sd1 ← standard deviation(F1 ) sd2 ← standard deviation(F2 ) return cov/(sd1 sd2 ) The representation of sequences in BioPerl does not include any method to compute the linear correlation coefficient of the k-mer frequencies of two sequences. However, the previous algorithm can be easily implemented in Perl by first implementing methods to compute the mean and standard deviation of an array of values and the covariance of two arrays of values.

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