By Gary Chartrand, Ping Zhang

ISBN-10: 0486483681

ISBN-13: 9780486483689

Written through of the main favorite figures in the sector of graph idea, this complete text provides a remarkably student-friendly procedure. aimed toward undergraduates taking a primary path in graph idea, its sound but available therapy emphasizes the heritage of graph conception and offers unique examples and lucid proofs. 2004 variation.

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Extra info for A First Course in Graph Theory (Dover Books on Mathematics)

Sample text

2 Distributing Presents Suppose we have n different presents, which we want to distribute to k children, where for some reason, we are told how many presents each child should get. So Adam should get nAdam presents, Barbara, nBarbara presents, etc. In a mathematically convenient (though not very friendly) way, we call the children 1, 2, . . , k; thus we are given the numbers (nonnegative integers) n1 , n2 , . . , nk . We assume that n1 + n2 + · · · + nk = n, else there is no way to distribute all the presents and give each child the right number of them.

Possible ways, etc. So the number of ways the presents can be laid out (given the distribution of the presents to the children) is a product of factorials: n1 ! · n2 ! · · · nk ! Thus the number of ways of distributing the presents is n! n2 ! · · · nk ! 1 We can describe the procedure of distributing the presents as follows. First, we select n1 presents and give them to the first child. This can be done in n ways. Then we select n2 presents from the remaining n − n1 and give them n1 to the second child, etc.

We compute the total sum of entries in this table in two different ways. First, what are the row sums? We get 1 for Al and 0 for everybody else. This is not a coincidence. If we consider a student like Al, who does not have any picture, then this student contributes to the bonus column, but nowhere else, which means that the sum in the row of this student is 1. Next, consider Ed, who has all 3 pictures. He has a 1 in the bonus column; in the next 3 columns he has 3 terms that are −1. In each of the next 3 columns he has a 1, one for each pair of pictures; it is better to think of this 3 as 32 .

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A First Course in Graph Theory (Dover Books on Mathematics) by Gary Chartrand, Ping Zhang


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