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S.V.R. Madabhushi, S. Lakshmivarahan, S.K. Dhall, "A Note on Orthogonal Graphs," IEEE Transactions on Computers, vol. 42, no. 5, pp. 624630, May, 1993.  
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@article{ 10.1109/12.223683, author = {S.V.R. Madabhushi and S. Lakshmivarahan and S.K. Dhall}, title = {A Note on Orthogonal Graphs}, journal ={IEEE Transactions on Computers}, volume = {42}, number = {5}, issn = {00189340}, year = {1993}, pages = {624630}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.223683}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  A Note on Orthogonal Graphs IS  5 SN  00189340 SP624 EP630 EPD  624630 A1  S.V.R. Madabhushi, A1  S. Lakshmivarahan, A1  S.K. Dhall, PY  1993 KW  bary hypercubes; interconnection schemes; conflictfree orthogonal memory access; multiprocessor design; connection mode; orthogonal graphs; Cayley graphs; vertex symmetric; shortest path routing algorithm; node disjoint paths; binary hypercube; graph theory; hypercube networks; parallel algorithms. VL  42 JA  IEEE Transactions on Computers ER   
Orthogonal graphs are natural extensions of the classical binary and bary hypercubes b=2/sup l/ and are abstractions of interconnection schemes used for conflictfree orthogonal memory access in multiprocessor design. Based on the type of connection mode, these graphs are classified into two categories: those with disjoint and those with nondisjoint sets of modes. The former class coincides with the class of bary b=2/sup l/ hypercubes, and the latter denotes a new class of interconnection. It is shown that orthogonal graphs are Cayley graphs, a certain subgroup of the symmetric (permutation) group. Consequently these graphs are vertex symmetric, but it turns out that they are not edge symmetric. For an interesting subclass of orthogonal graphs with minimally nondisjoint set of modes, the shortest path routing algorithm and an enumeration of node disjoint (parallel) paths are provided. It is shown that while the number of node disjoint paths is equal to the degree, the distribution is not uniform with respect to Hamming distance as in the binary hypercube.
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