Shields-Harary numbers of graphs with respect to continuous concave cost functions
نویسندگان
چکیده
منابع مشابه
Shields-harary Numbers of Graphs with Respect to Continuous Concave Cost Functions
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 ...
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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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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2003
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171203212059