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The English term monograph is derived from modern Latin monographia, which has its root in Greek. [1] In the English word, mono-means ' single ' and -graph means ' something written '. [2] Unlike a textbook, which surveys the state of knowledge in a field, the main purpose of a monograph is to present primary research and original scholarship ...
The 1980 monograph Spectra of Graphs [16] by Cvetković, Doob, and Sachs summarised nearly all research to date in the area. In 1988 it was updated by the survey Recent Results in the Theory of Graph Spectra. [17] The 3rd edition of Spectra of Graphs (1995) contains a summary of the further recent contributions to the subject. [15]
Monographic series (alternatively, monographs in series) are scholarly and scientific books released in successive volumes, each of which is structured like a separate book or scholarly monograph. A volume in the Loeb Classical Library. Each installment in this monographic series is devoted to a Greek or Latin author, and is accompanied by ...
Resolving sets for graphs were introduced independently by Slater (1975) and Harary & Melter (1976), while the concept of a resolving set and that of metric dimension were defined much earlier in the more general context of metric spaces by Blumenthal in his monograph Theory and Applications of Distance Geometry. Graphs are special examples of ...
The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has i vertices. [6] Ringel's conjecture asks if the complete graph K 2n+1 can be decomposed into copies of any tree ...
Similarly, if G is a group acting on a tree X without edge-inversions (that is, so that for every edge e of X and every g in G we have ge ≠ e), one can define the natural notion of a quotient graph of groups A. The underlying graph A of A is the quotient graph X/G.
A complete bipartite graph of K 4,7 showing that Turán's brick factory problem with 4 storage sites (yellow spots) and 7 kilns (blue spots) requires 18 crossings (red dots) For any k, K 1,k is called a star. [2] All complete bipartite graphs which are trees are stars. The graph K 1,3 is called a claw, and is used to define the claw-free graphs ...
A graph with three components. In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting ...