Operator Decomposition of Graphs and the Reconstruction Conjecture |
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Affiliation: | 1. KFUPM, KSA;2. Aramco Engineer, KSA;1. EötvösLoránd University ELTE, PázmányPétersétány 1/C, Budapest, 1117, Hungary |
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Abstract: | We present a new type of decomposition of graphs – the operator decomposition connected with the classical notion of homogeneous set (or module). Using this decomposition we prove that Kelly-Ulam reconstruction conjecture is true for graphs having homogeneous set with prescribed properties, as well as for non-p-connected graphs. |
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