Graph Compositions and Flats of Cycle Matroids

Mphako-Banda, Eunice

doi:10.2989/qm.2009.32.4.2.960

Cited by 2 publications

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“…The relationship between graph compositions and flats of cycle matroids were established in [5]. We state the following theorems without proof; for details, we refer to [5].…”

Section: Relationship Between Graph Compositions and Flats Of Cycle Matroidsmentioning

confidence: 99%

Graph compositions of suspended $Y$-trees

Mphako-Banda¹,

Werner²

2016

Rocky Mountain J. Math.

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We count the number of graph compositions of suspended Y -trees via flats of the cycle matroid of the suspended Y -trees. 1. Introduction. The notion of graph composition was introduced by Knopfmacher and Mays in [3]. In this original work, various formulas, generating functions and recurrence relations for composition counting functions are given for several families of graphs. Graph compositions play an important role in the generalization of both ordinary compositions of positive integers and partitions of finite sets.This work is extended further to bipartite graphs, as well as some operations on graphs, including unions of graphs and the 2-sum of graphs in [1, 2, 7]. In [4], the terminology of graph composition is explored further, but under a new term, comppartition. In [5], it is shown that the number of graph compositions is equal to the total number of flats of the cycle matroid.The number of compositions for the following graphs are given in [3]:(i) T n : a tree on n vertices, (ii) P n : a path with n vertices, (iii) S n : a star graph on n vertices, (iv) K n : a complete graph on n vertices, (v) C n : a cycle graph on n vertices, (vi) W n : a wheel on n vertices, (vii) L n : a ladder graph on 2n vertices, and (viii) K m,n : a complete bipartite graph.In particular, it is shown that C(T n ) = C(P n ) = C(S n ) = 2 n−1 .

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“…The relationship between graph compositions and flats of cycle matroids were established in [5]. We state the following theorems without proof; for details, we refer to [5].…”

Section: Relationship Between Graph Compositions and Flats Of Cycle Matroidsmentioning

confidence: 99%