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Factor and fractional factor are widely used in many fields related to computer science. The isolated toughness of an incomplete graph G is defined as iτThis parameter has a close relationship with the existence of factors and fractional factors of graphs. In this paper, we pay our attention to computational complexity of isolated toughness, and present an optimal polynomial time algorithm to compute the isolated toughness for interval graphs, a subclass of cocomparability graphs.

The isolated scattering number of an incomplete connected graph G is defined as isc(G) = max{i(G − X) − |X| : X ∈ C(G)}, where i(G − X) and C(G), respectively, denote the number of components which are isolated vertices and the set of all separators of G. The isolated scattering number is a comparatively better parameter to measure the vulnerability of networks. We give a polynomial time algorithm to compute the isolated scattering number of interval graphs, a subclass of co-comparability graphs. Our result can also be used to compute isolated scattering number of proper interval graph.

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