COGRAPH Meaning and
Definition
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A cograph is a mathematical structure, particularly a type of graph, which is defined as the complement of a disjoint union of graphs or as the graph obtained by a certain class of operations performed solely on complete graphs.
In more precise terms, a cograph is a finite undirected graph that can be generated recursively by either taking a single vertex graph as its base case or by forming the disjoint union or the join of two smaller cographs. The complement of a cograph is also a cograph.
Cographs hold a special position in graph theory as they possess several interesting properties. For instance, they are closed under taking induced subgraphs, meaning that any subgraph obtained from a cograph is also a cograph. This property makes cographs useful in various algorithmic applications like network analysis and circuit design. Moreover, cographs are characterized by a specific graph decomposition called cotree, which enables efficient construction and manipulation of cographs.
The concept of cographs dates back to the 1960s when it was introduced by Maurice Nivat and Claude Puech as a generalization of complete graphs. Since then, cographs have been extensively studied and have found numerous applications in diverse fields such as computer science, operations research, and biology.
Common Misspellings for COGRAPH
- sograph
- xograph
- vograph
- fograph
- dograph
- cigraph
- ckgraph
- clgraph
- cpgraph
- c0graph
- c9graph
- cofraph
- covraph
- cobraph
- cohraph
- coyraph
- cotraph
- cogeaph
- cogdaph
- cogfaph
Etymology of COGRAPH
The word "cograph" is a combination of two parts: "co-" and "-graph".
The prefix "co-" comes from the Latin word "cum", which means "with" or "together". In English, "co-" is often used to indicate partnership, cooperation, or mutual action.
The suffix "-graph" is derived from the Greek word "graphos", meaning "to write" or "to draw". It is commonly used to refer to written or drawn representations or records.
Combining these two components, "cograph" suggests a collective or collaborative representation or record. In specific contexts, such as in graph theory, a "cograph" refers to a type of graph where two graphs are combined in specified ways.
