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The (n,k)-star graph is a very important computer modelling. The independent number and chromatic number of a graph are two important parameters in graph theory. However, we did not know the values of this two parameters of the (n,k)-star graph since it was proposed. In [18], Wei et. al. declared that they determined the independent number of the (n,k)-star graph, unfortunately their proof is wrong. This paper generalize their result and present a maximum independent sets partition of (n,k)-star graph. From that we can immediately deduce the exact value of the independent number and chromatic number of (n,k)-star graph.

complexity

Maximum Independent Sets Partition of (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:math>)-Star Graphs

Maximum Independent Sets Partition of (n,k)-Star Graphs