Distinct vertices in g d are adjacent, if their distance in g is at most d. The hamming distance between two vectors is the number of positions in which the two. What are some good books for selfstudying graph theory. O r 1993 applied and algorithmic graph theory new york. Hamming graphs are a special class of graphs named after richard hamming and used in.
On the canonical metric representation, average distance, and. The doob graph is the graph given by the graph cartesian product of copies of the shrikhande graph with a hamming graph. Average distance of a graph is expressed in terms of its canonical metric representation. Cartesian product of complete graphs is a hamming graph. A graph is an binary hamming graph if its vertices can be labelled by fixed length. Unsolved problems in graph theory arising from the study of codes n. For any terms and concepts not defined here we refer to the books 8, 14. The hamming graph hd,q has vertex set s d, the set of ordered dtuples of elements of s, or sequences of length d from s. Purchase includes a free trial membership in the publishers book club where you can select from more than a million books without charge.
Free graph theory books download ebooks online textbooks. The distance power g d of a graph g has the same vertex set as g. The hamming graph hd,q is, equivalently, the cartesian product of d complete graphs k q. Graph theory lecture notes pennsylvania state university.
It is clear that a short survey cannot cover all aspects of metric graph theory that are. Two fundamental questions in coding theory two of the most basic questions in coding theory are. Find the hamming distances between two or more graphs. Graph theory notes vadim lozin institute of mathematics university of warwick 1 introduction a graph g v. In information theory, the hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. The hamming index of the graph g is the sum of hamming distances. In mathematics and computer science, graph edit distance ged is a measure of similarity or. Two vertices are adjacent if they differ in precisely one coordinate. Hamming distance and jarowinkler distance may be interpreted as graph edit distances. A hamming graph is the cartesian product of complete graphs and a partial. Computational and mathematical organization theory, 114. Check our section of free ebooks and guides on graph theory now. Let a q n, d be the maximum order maximum number of codewords of a qary code of length n and hamming distance at least d.
Graph theory researchers were first interested in the problem of. Diestel is excellent and has a free version available online. Colorings of hammingdistance graphs uknowledge university. On hamming index generated by adjacency matrix of graphs. In other words, it measures the minimum number of substitutions required to change one string into the other, or the minimum number of errors that could have transformed one string into the other. This page contains list of freely available ebooks, online textbooks and tutorials in. Edit distance between 2 strings the levenshtein distance. Firstorder logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. Hamming graphs are used in coding theory and have appli. Unsolved problems in graph theory arising from the study. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how.