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incidence matrix with respect to an orientation (Definition)

Let $ G$ be a finite graph with $ n$ vertices, $ \{v_1, \ldots, v_n\}$ and $ m$ edges, $ \{e_1, \ldots, e_m\}$. For each edge $ e = (v_i,v_j)$ of $ G$ choose one vertex to be the positive end and the other to be the negative end. In this way, we assign an orientation to $ G$. The incidence matrix of $ G$ with respect an orientation is an $ n \times m$ matrix $ D=(d_{ij})$ where

$\displaystyle d_{ij} = \left\{ \begin{array}{ll} +1 & \textrm{if $v_i$\ is the ... ... is the negative end of $e_j$} \ 0 & \textrm{otherwise}. \end{array} \right. $



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Also defines:  orientation
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Cross-references: matrix, negative, positive, vertex, edges, vertices, graph, finite
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This is version 3 of incidence matrix with respect to an orientation, born on 2007-05-14, modified 2007-05-14.
Object id is 9382, canonical name is IncidenceMatrixWithRespectToAnOrientation.
Accessed 949 times total.

Classification:
AMS MSC05C50 (Combinatorics :: Graph theory :: Graphs and matrices)

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