By Gary Chartrand, Ping Zhang
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.
Read Online or Download A First Course in Graph Theory (Dover Books on Mathematics) PDF
Similar graph theory books
This self-contained ebook examines effects on transfinite graphs and networks completed via a continuous study attempt in the past numerous years. those new effects, overlaying the mathematical idea of electric circuits, are diversified from these awarded in formerly released books by way of the writer, Transfiniteness for Graphs, electric Networks, and Random Walks and Pristine Transfinite Graphs and Permissive electric Networks.
Algorithmic Graph thought and ideal Graphs, first released in 1980, has develop into the vintage advent to the sphere. This new Annals version maintains to show the message that intersection graph versions are an important and significant device for fixing real-world difficulties. It continues to be a stepping stone from which the reader could embark on one of the interesting study trails.
This textbook offers an advent to the Catalan numbers and their outstanding homes, in addition to their a number of purposes in combinatorics. Intended to be obtainable to scholars new to the topic, the booklet starts with extra easy subject matters earlier than progressing to extra mathematically subtle themes.
- Mathematics and computer science 3: algorithms, trees, combinatorics and probabilities
- Finance, Economics, and Mathematics
- Color-Induced Graph Colorings
- Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization
- Graphs: Theory and Algorithms
- Coloring Mixed Hypergraphs. Theory, Algorithms and Applications
Extra info for A First Course in Graph Theory (Dover Books on Mathematics)
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 .
A First Course in Graph Theory (Dover Books on Mathematics) by Gary Chartrand, Ping Zhang