Shields-harary Numbers of Graphs with Respect to Continuous Concave Cost Functions
نویسندگان
چکیده
The Shields-Harary numbers are a class of graph parameters thatmeasure a certain kind of robustness of a graph, thought of as a network of fortified reservoirs, with reference to a given cost function. We prove a result about the Shields-Harary numbers with respect to concave continuous cost functions which will simplify the calculation of these numbers for certain classes of graphs, including graphs formed by two intersecting cliques, and complete multipartite graphs.
منابع مشابه
The Shields-Harary numbers of Km, n for continuous concave cost functions vanishing at 1
It is shown that the Shields–Harary index of vulnerability of the complete bipartite graph Km,n, with respect to the cost function f (x)= 1− x, 0 x 1, is m, if n m+ 2√m, and 1 n+1 (n+m) 2 4 , ifm n<m+ 2 √ m. It follows that the Shields–Harary number ofKm,n with respect to any concave continuous cost function f on [0, 1] satisfying f (1)=0 ismf (0), if n m+2√m, and between 1 n+1 (n+m) 2 4 f (0) ...
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