PlanetMath: incidence matrix with respect to an orientation

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incidence matrix with respect to an orientation

(Definition)

Let be a finite graph with vertices, $\{v_1, \ldots, v_n\}$ and edges, $\{e_1, \ldots, e_m\}$ . For each edge of choose one vertex to be the positive end and the other to be the negative end. In this way, we assign an orientation to . The incidence matrix of 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.$

"incidence matrix with respect to an orientation" is owned by Mathprof.

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Also defines:

orientation

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Cross-references: matrix, negative, positive, vertex, edges, vertices, graph, finite
There are 9 references to this entry.

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 MSC:

05C50 (Combinatorics :: Graph theory :: Graphs and matrices)

Pending Errata and Addenda

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