{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T15:34:55Z","timestamp":1776008095455,"version":"3.50.1"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,4]]},"abstract":"<jats:p> We study the problem of using mobile guards to defend the vertices of a graph [Formula: see text] against a single attack on its vertices. A vertex cover of a graph [Formula: see text] is a set [Formula: see text] such that for each edge [Formula: see text], at least one of [Formula: see text] or [Formula: see text] is in [Formula: see text]. The minimum cardinality of a vertex cover is termed the vertex covering number and it is denoted by [Formula: see text]. In this context, we introduce a new protection strategy called the secure vertex cover[Formula: see text]SVC[Formula: see text] problem, where the guards are placed at the vertices of a graph, in order to protect the graph against a single attack on its vertices. We are concerned with the protection of [Formula: see text] against a single attack, using at most one guard per vertex and require the set of guarded vertices to be a vertex cover. In addition, if any guard moves along an edge to deal with an attack to an unguarded vertex, then the resulting placement of guards must also form a vertex cover. Formally, this protection strategy defends the vertices of a graph against a single attack and simultaneously protects the edges. We define a SVC to be a set [Formula: see text] such that [Formula: see text] is a vertex cover and for each [Formula: see text], there exists a [Formula: see text] such that [Formula: see text] is a vertex cover. The minimum cardinality of an SVC is called the secure vertex covering number and it is denoted by [Formula: see text]. In this paper, a few properties of SVC of a graph are studied and specific values of [Formula: see text] for few classes of well-known graphs are evaluated. <\/jats:p>","DOI":"10.1142\/s1793830917500264","type":"journal-article","created":{"date-parts":[[2017,2,17]],"date-time":"2017-02-17T08:08:26Z","timestamp":1487318906000},"page":"1750026","source":"Crossref","is-referenced-by-count":4,"title":["Secure vertex cover of a graph"],"prefix":"10.1142","volume":"09","author":[{"given":"P. Roushini Leely","family":"Pushpam","sequence":"first","affiliation":[{"name":"Department of Mathematics, D.B. 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