Edge, vertex and mixed fault-diameters

Iztok Banič (Author), Rija Erveš (Author), Janez Žerovnik (Author)

Abstract

Let ▫${\mathcal{D}}^E_q(G)$▫ denote the diameter of a graph ▫$G$▫ after deleting any of its ▫$q$▫ edges, and ▫${\mathcal{D}}^V_p(G)$▫ denote the diameter of ▫$G$▫ after deleting any of its ▫$p$▫ vertices. We prove that ▫${\mathcal{D}}^E_a(G) \le {\mathcal{D}}^V_a(G) + 1$▫ a for all meaningful ▫$a$▫. We also define mixed fault diameter ▫${\mathcal{D}}^M_{(p,q)}(G)$▫, where ▫$p$▫ vertices and ▫$q$▫ edges are deleted at the same time. We prove that for ▫$0 < l \le a$▫, ▫${\mathcal{D}}^E_a(G) \le {\mathcal{D}}^M_{(a-l,l)}(G) \le {\mathcal{D}}^V_a(G) + 1$▫, and give some examples.

Keywords

matematika;teorija grafov;povezanost;mathematics;(vertex)-connectivity;edge-connectivity;(vertex) fault-diameter;edge-fault diameter;interconnection network;

Data

Language:	English
Year of publishing:	2008
Typology:	0 - Not set
Organization:	UL FS - Faculty of Mechanical Engineering
UDC:	519.17
COBISS:	14912345
ISSN:	1318-4865
Views:	769
Downloads:	76
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Secondary keywords:	matematika;teorija grafov;povezanost;
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 1-10
Volume:	ǂVol. ǂ46
Issue:	ǂšt. ǂ1058
Chronology:	2008
ID:	67474