A class of threshold and domishold graphs: equistable and equidominating graphs
β Scribed by Charles Payan
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 484 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
A thwahold grerph (rtzspativ4y domlshukf graph) is 01 graph for which the independent 881% (rapsctiwzly ths dominuting a&a) cctn bgr chnfuctsrixsd by the 0, l-aolutiona of a linaur
kpallty (ass [ij and [S]),
We define here the #rugher far which the mawlmal indapsndent eettr (rsopsctivsly tha mlnlmul dominating o&a) IP~ ehnneteriazd by the 0, l~nalutien# of tl linar equation, Such grlrphn UPC rraid ts be equlstabk (renpeetiv4y aqstkfomlnafln~),
We chatxu&zriz@ (by their urehitcaetural ntruetufct und by forbidden induead nubaruphn) thrsnheld grtrphn und dominhald grtlphn which ufe aquintrrbltr or ~quidcrminuting~ A lunger elrrnn af equintubls graphn irr ulna prsnentad,
π SIMILAR VOLUMES
## Abstract In this paper, we prove the following result: Every graph obtained by connecting (with any number of edges) two vertexβdisjoint upperβembeddable graphs graphs with even Betti number is upperβembeddable.
## Abstract In this paper, we show that __n__ β©Ύ 4 and if __G__ is a 2βconnected graph with 2__n__ or 2__n__β1 vertices which is regular of degree __n__β2, then __G__ is Hamiltonian if and only if __G__ is not the Petersen graph.
The idea of u t i Z i z i n g the connectivity properties of a graph as measures of i t s vulnerability has been welZ docwnented. graph t h e o r e t i c concepts and the b a s i c resuZts of t h i s theory are r e v i m e d here. are defined and compared. SpecificaZZy a class of graphs called teZe