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A Survey on Complexity of Integrity Parameter | ||
| Journal of Algorithms and Computation | ||
| مقاله 1، دوره 47، شماره 1، شهریور 2016، صفحه 11-19 اصل مقاله (669.39 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jac.2016.7931 | ||
| نویسنده | ||
| Mahmood Shabankhah* | ||
| University of Tehran, College of Engineering, Department of Engineering Science | ||
| چکیده | ||
| Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. In this paper we discuss Integrity and its properties in vulnerability calculation. The integrity of a graph G, I(G), is defined to be min(| S | +m(G − S)) where S ⊂ V (G) and m(G − S) is the maximum order of the components of G − S. Similarly the edge-integrity of G is I′(G) := min(| S | +m(G − S)) where now S ⊆ E(G). Here and through the remaining sections, by an I-set (with respect to some prescribed graph G) we will mean a set S ⊂ V (G) for which I(G) =| S | +m(G − S). We define an I′-set similarly. In this paper we show a lower bound on the edgeintegrity of graphs and present an algorithm for its computation. | ||
| کلیدواژهها | ||
| Integrity parameter؛ toughness؛ neighborconnectivity؛ mean integrity؛ edge-connectivity vector؛ l-connectivity and tenacity | ||
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