In this paper, we define an α-almost (k; 2e + 1)-separable matrix and an α-almostke-disjunct matrix. Using their complements, we devise algorithms for fault-tolerant trivial two-stage group tests (pooling designs) for k-complexes. We derive the expected values for the given algorithms to identify all such positive complexes.

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The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Line graphs play an important role in the study of graph theory. Generalized line graphs extend the ideas of both line graphs and cocktail party graphs. In this paper, we establish relations between the energy of the generalized line graph of a graph G and the Laplacian and signless Laplacian energies of G. We give upper and lower bounds for the energy of generalized line graphs. Finally, we present upper and lower bounds for some special graphs.