Search results for "05c07"
showing 3 items of 3 documents
Extremal Irregular Digraphs
2018
A digraph is called irregular if its distinct vertices have distinct degree pairs. An irregular digraph is called minimal (maximal) if the removal of any arc (addition of any new arc) results in a non-irregular digraph. It is easily seen that the minimum sizes among irregular n-vertex whether digraphs or oriented graphs are the same and are asymptotic to (√2/3) n3/2; maximum sizes, however, are asymptotic to n2 and n2/2, respectively. Let s stand for the sum of initial positive integers, s = 1, 3, 6, . . . . An oriented graph Hs and a digraph Fs, both large (in terms of the size), minimal irregular, and on any such s vertices, s ≥ 21, are constructed in [Large minimal irregular digraphs, Op…
Miscellaneous Graph Preliminaries
2020
Summary This article contains many auxiliary theorems which were missing in the Mizar Mathematical Library [2] to the best of the author’s knowledge. Most of them regard graph theory as formalized in the GLIB series (cf. [8]) and most of them are preliminaries needed in [7] or other forthcoming articles.
Refined Finiteness and Degree Properties in Graphs
2020
Summary In this article the finiteness of graphs is refined and the minimal and maximal degree of graphs are formalized in the Mizar system [3], based on the formalization of graphs in [4].