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On the nonsingular submatrices of the incidence matrix of a graph over the real field

โœ Scribed by Wai-Kai Chen

Publisher
Elsevier Science
Year
1970
Tongue
English
Weight
872 KB
Volume
289
Category
Article
ISSN
0016-0032

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โœฆ Synopsis

The nonsingular submatrices of maximum order of the complete and the reduced incidence matrices over the real jield of a graph are shown to be in one-to-one correspondence with the odd generalized circuits and the odd generalized k-trees of the graph, respectively.

It is also shown that the positive terms irt the final expansions of a unisignant and its cofactors correspond to these subgraphs.

Thus, a technique for enumerating aE.8 the positive terms without duplication is obtained.

The extension to digraphs is also considered, and illustrative examples are given.

๐Ÿ“œ SIMILAR VOLUMES

On the distance matrix of a directed gra
On the distance matrix of a directed graph
โœ R. L. Graham; A. J. Hoffman; H. Hosoya ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 144 KB ๐Ÿ‘ 2 views

## Abstract In this note, we show how the determinant of the distance matrix __D(G__) of a weighted, directed graph __G__ can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks __G~i~__ of __G__. In particular, when cof __D(G__), the sum of the cofactors of _