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The Petersen graph is a cubic graph. The complete bipartite graph, is an example of a bicubic graph. In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs.
He is considered as one of pioneers of chemical graph theory. The first book about this interdisciplinary field was edited by Balaban and appeared in 1976: Chemical Applications of Graph Theory. One area in which cubic (or trivalent) graphs play a dominant role is the enumeration of [n]annulene valence isomers (CH) n where n is an even
In chemistry, polyvalency (or polyvalence, multivalency) is the property of molecules and larger species, such as antibodies, medical drugs, and even nanoparticles surface-functionalized with ligands, like spherical nucleic acids, that exhibit more than one supramolecular interaction.
Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena. [1] The pioneers of chemical graph theory are Alexandru Balaban, Ante Graovac, Iván Gutman, Haruo Hosoya, Milan Randić and Nenad Trinajstić [2] (also Harry Wiener and others). In 1988, it was ...
Regular graphs of degree at most 2 are easy to classify: a 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of a disjoint union of cycles and infinite chains. A 3-regular graph is known as a cubic graph.
This leaves the other graphs in the 3-connected class because each 3-regular graph can be split by cutting all edges adjacent to any of the vertices. To refine this definition in the light of the algebra of coupling of angular momenta (see below), a subdivision of the 3-connected graphs is helpful.
In chemical graph theory and in mathematical chemistry, a molecular graph or chemical graph is a representation of the structural formula of a chemical compound in terms of graph theory. A chemical graph is a labeled graph whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds.
every cubic bridgeless graph without Petersen minor has a cycle double cover. [13] is the smallest cubic graph with Colin de Verdière graph invariant μ = 5. [14] is the smallest graph of cop number 3. [15] has radius 2 and diameter 2. It is the largest cubic graph with diameter 2. [b] has 2000 spanning trees, the most of any 10-vertex cubic ...