The orders of graphs with prescribed degree sets
β Scribed by Timothy A. Sipka
- Publisher
- John Wiley and Sons
- Year
- 1980
- Tongue
- English
- Weight
- 321 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
The degree set π^G^ of a graph G is the set of degrees of the vertices of G. For a finite nonempty set S of positive integers, all positive integers p are determined for which there exists a graph G of order p such that π^G^ = S.
π SIMILAR VOLUMES
d 2,n 2 ) is a bipartite graphical sequence, if there is a bipartite graph G with degrees {D 1 , D 2 } (i.e., G has two independent vertex sets In other words, {D 1 , D 2 } is a bipartite graphical sequence if and only if there is an n 1 1 n 2 matrix of 0's and 1's having d 1j 1 1's in row j 1 and
## Abstract It is well known that certain graphβtheoretic extremal questions play a central role in the study of communication network vulnerability. Herein we consider a generalization of some of the classical results in this area. We define a (__p__, Ξ, Ξ΄, Ξ») graph as a graph having __p__ points,
## Abstract Ε irΓ‘Ε constructed infinite families of __k__βcrossingβcritical graphs for every __k__β©Ύ3 and Kochol constructed such families of simple graphs for every __k__β©Ύ2. Richter and Thomassen argued that, for any given __k__β©Ύ1 and __r__β©Ύ6, there are only finitely many simple __k__βcrossingβcriti
Suppose that the graphical partition H(A) = (a: 2 . . . 2 a:) arises from A = (al 2 . . . 2 a,) by deleting the largest summand a1 from A and reducing the a1 largest of the remaining summands by one. Let (a;+l 2 . . 2 ah) = H ( A ) denote the partition obtained by applying the operator H i times. We