{"product_id":"critical-and-maximal-directed-graphs-von-gennady-fridman","title":"Critical and Maximal Directed Graphs","description":"\u003cp\u003eIn this Memoir we investigate finite directed graphs (digraphs) without loops with extreme properties with respect to certain metric or quasi-metric functionals. An n-vertex digraph G is called critical with respect to some functional F if adding an arbitrary missing arc to G results in decreasing F, and maximal if G has the maximum number of arcs among all n-vertex digraphs with the same value of F. The distance from a vertex x to a vertex y in the digraph G equals the minimum number of arcs in a directed path from x to y; if there are no directed path from x to y, then the distance is infinite. The quasi-distance between x and y is defined as the minimum of distances from x to y and from y to x. We also define in the usual way diameter, radius and, similarly, quasi-diameter and quasi-radius of the digraph G. We characterize up to isomorphism the critical digraphs with infinite value of diameter, radius, quasi-diameter and quasi-radius. Moreover, the maximal digraphs with finite value of radius and quasi-diameter are studied. And we leave the problem of describing the maximal digraphs with finite quasi-radius to the next generation.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9786139819188\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9786139819188","offer_id":39446795812957,"sku":"9786139819188","price":35.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/9ae75fae-8490-4f47-9ca5-0af6648b9ee6.jpg?v=1773732434","url":"https:\/\/shop.autorenwelt.de\/products\/critical-and-maximal-directed-graphs-von-gennady-fridman","provider":"Autorenwelt Shop","version":"1.0","type":"link"}