Ueda, T., Circular nonsingular threshold transformations, Discrete Mathematics 105 (1992) 249-258. Circular n-dimensional Boolean transformations are those which commute with an n-cyclic permutation of variables. A minimal Boolean transformation is the one which has the minimum number of coordinates
Graphs of nonsingular threshold transformations
β Scribed by Takao Ueda
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 695 KB
- Volume
- 128
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
After the graph structures of self-dual nonsingular (i.e. one-to-one) transformations of (0, 1)" are described, a construction method of generating minimal nonsingular threshold transformations from lower-dimensional ones is presented. Theorems which concern nonsingular threshold transformations and support that procedure are also proved. Then, in addition to circular, nonsingular transformations in the author's previous paper, five classes of noncircular, nonsingular threshold transformations are given with their graph structures.
π SIMILAR VOLUMES
For simple r-regular graph, an edge-reduction and three transformations (S-, X-, and ~-transformations) are defined which preserve the regularity. In the case r = 3, relations between them are discussed and it is proved that for any two connected cubic graphs with the same order one is obtained from
## Abstract The threshold weight of a graph __G__ is introduced as a measure of the amount by which __G__ differs from being a threshold graph. The threshold graphs are precisely the graphs whose threshold weights are 0. At the opposite extreme is the class of graphs for which the threshold weight
## Abstract We prove that the strong product of any at least ${({\rm ln}}\, {2})\Delta+{O}(\sqrt{\Delta})$ nonβtrivial connected graphs of maximum degree at most Ξ is pancyclic. The obtained result is asymptotically best possible since the strong product of β(lnβ2)__D__β stars __K__~1,__D__~ is not