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Algebraic characterization of skeletal branching

✍ Scribed by Ivan Gutman; Milan Randić

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
380 KB
Volume
47
Category
Article
ISSN
0009-2614

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✦ Synopsis

An algebraic charactcrlzatlon of branching of skeletal forms is proposed which IS based on the concept of the comparability of functions as defined by Muirhead. The approach allows a rigorous definition of the concept of branch@ and susgests that structures having an identical distribution of valencies should not be discriminated. In addition situations arise when skeletal forms having a different valency configuration cannot be compared. It is discussed how this helps in clarifying ambiguities concerning branching.

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## Abstract A cycle in a graph is a set of edges that covers each vertex an even number of times. A cocycle is a collection of edges that intersects each cycle in an even number of edges. A bicycle is a collection of edges that is both a cycle and a cocycle. The cycles, cocycles, and bicycles each