کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6423794 | 1632593 | 2011 | 6 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Chip-Firing and Riemann-Roch Theory for Directed Graphs Chip-Firing and Riemann-Roch Theory for Directed Graphs](/preview/png/6423794.png)
Baker and Norine developed a graph theoretic analogue of the classical Riemann-Roch theorem. Amini and Manjunath extended their criteria to all full-dimensional lattices orthogonal to the all ones vector. We show that Amini and Manjunathʼs criteria holds for all full-dimensional lattices orthogonal to some positive vector and study some combinatorial examples of such lattices. Two distinct generalizations of the chip-firing game of Baker and Norine to directed graphs are provided. We describe how the “row” chip-firing game is related to the sandpile model and the “column” chip-firing game is related to directed G-parking functions. We finish with a discussion of arithmetical graphs, introduced by Lorenzini, viewing them as a class of vertex weighted graphs whose Laplacian is orthogonal to a positive vector and describe how they may be viewed as a special class of unweighted strongly connected directed graphs.
Journal: Electronic Notes in Discrete Mathematics - Volume 38, 1 December 2011, Pages 63-68