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We study the problem of adding edges to a given arbitrary graph so that the resulting graph is a split graph, called a split completion of the input graph. Our purpose is to add an inclusion minimal set of edges to obtain a minimal split completion, which means that no proper subset of the added edges is sufficient to create a split completion. Minimal completions of arbitrary graphs into chordal graphs have been studied previously, and new results have been added continuously. There is an increasing interest in minimal completion problems, and minimal completions of arbitrary graphs into interval graphs have been studied very recently. We extend these previous results to split graphs, and we give a characterization of minimal split completions, along with a linear time algorithm for computing a minimal split completion of an arbitrary input graph. Among our results is a new way of partitioning the vertices of a split graph uniquely into three subsets.

Abstract-mHealth is having a profound and increasing impact on the delivery of medical and health services using mobile devices. However, many existing mHealth systems do not systematically address the security issues involved. As sensitive information is stored, exchanged and processed in these systems, issues like privacy, authentication, secure storage, accountability and permissions must be given top priority. In this paper we propose a protocol that provides end-to-end security, encrypted data storage and recovery mechanisms on mobile devices. We use openXdata as our reference mHealth system.

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