A characterization of the edge connectivity of direct products of graphs

Abstract

V članku dokažemo formulo za povezanost po povezavah direktnega produkta grafov. V formuli se povezanost po povezavah produkta izraža kot funkcija povezanosti po povezavah, najmanjše stopnje, števila povezav in dvodelne frustracije obeh faktorjev. Prav tako v članku opišemo strukturo najmanjših presečnih množic v direktnih produktih grafov.

Keywords

matematika;teorija grafov;direktni produkt;povezanost po povezavah;mathematics;graph theory;direct product;edge connectivity;

Data

Language:	English
Year of publishing:	2013
Typology:	1.01 - Original Scientific Article
Organization:	UM FS - Faculty of Mechanical Engineering
UDC:	519.17
COBISS:	16649305
ISSN:	0012-365X
Views:	26
Downloads:	18
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Karakterizacija povezanosti po povezavah direktnih produktov grafov
Secondary abstract:	The direct product of graphs ▫$G = (V(G),E(G))$▫ and ▫$H = (V(H),E(H))$▫ is the graph, denoted as ▫$G \times H$▫, with vertex set ▫$V(G \times H) = V(G) \times V(H)$▫, where vertices ▫$(x_1,y_1)$▫ and ▫$(x_2,y_2)$▫ are adjacent in ▫$G \times H$▫ if ▫$x_1x_2 \in E(G)$▫ and ▫$y_1y_2 \in E(H)$▫. The edge connectivity of a graph ▫$G$▫, denoted as ▫$\lambda(G)$▫, is the size of a minimum edge-cut in ▫$G$▫. We introduce a function ▫$\psi$▫ and prove the following formula ▫$$\lambda (G \times H) = \min \{2\lambda(G)\|E(H)\|, 2\lambda(H)\|E(G)\|, \delta(G \times H), \psi(G,H), \psi(H,G)\} .$$▫ We also describe the structure of every minimum edge-cut in ▫$G \times H$▫.
Type (COBISS):	Not categorized
Pages:	str. 1385-1393
Volume:	Vol. 313
Issue:	iss. 12
Chronology:	2013
ID:	1476882