The Path Matrix and its Realizability
- 1 September 1959
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IRE Transactions on Circuit Theory
- Vol. 6 (3) , 267-272
- https://doi.org/10.1109/TCT.1959.1086557
Abstract
This paper presents in one listing those properties of the path matrix of a graph which are fundamental and interesting in nature. Included are 1) a relation between the path matrix and the incidence matrix, 2) the rank of the path matrix, 3) relations between paths and cut sets, and 4) relations between paths and circuits (Ashenhurst's lemmas). Also included are a number of necessary conditions for the realizability of a matrix as a path matrix of a graph.Keywords
This publication has 4 references indexed in Scilit:
- On Realizability of a Circuit MatrixIRE Transactions on Circuit Theory, 1959
- On Electrical Circuits and Switching CircuitsIRE Transactions on Circuit Theory, 1956
- Topological Considerations in the Design of Driving-Point FunctionsIRE Transactions on Circuit Theory, 1955
- The solution of passive electrical networks by means of mathematical treesProceedings of the IEE - Part III: Radio and Communication Engineering, 1953