ON VULNERABILITY MEASURES OF NETWORKS

As links and nodes of interconnection networks are exposed to failures, one of the most important features of a practical networks design is fault tolerance. Vulnerability measures of communication networks are discussed including the connectivities, fault diameters, and measures based on Hosoya-Wiener polynomial. An upper bound for the edge fault diameter of product graphs is proved

Bounds on distance measures in graphs and altered graphs

Abstract: Please refer to full text to view abstract.D.Phil. (Mathematics and Applied Mathematics

Edge, vertex and mixed fault-diameters

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

EDGE, VERTEX AND MIXED FAULT-DIAMETERS

Let DE q (G) denote the diameter of a graph G after deleting any of its q edges, and DV p (G) denote the diameter of G after deleting any of its p vertices. We prove that DE a (G) ≤ DV a (G) + 1 for all meaningful a. We also define mixed fault diameter DM (p,q)(G), where p vertices and q edges are deleted at the same time. We prove that for 0 &lt; l ≤ a, DE a (G) ≤ DM (a−ℓ,ℓ)(G) ≤ DV a (G) + 1, and give some examples

Edge, vertex and mixed fault diameters of Cartesian graph products and bundels

V disertaciji raziskujemo povezanost in okvarne premere kartezičnih grafovskih svežnjev in kartezičnih produktov. Vpeljemo mešano povezanost in mešani okvarni premer grafa, ki posplošujeta povezanosti in okvarna premera definirana glede na eno vrsto okvarjenih elementov. Nekatere rezultate na kartezičnih grafovskih svežnjih in produktih glede na eno vrsto okvarjenih elementov posplošimo in v določenih primerih tudi izboljšamo.In dissertation we study connectivity and fault diameters of Cartesian graph products and bundles. We define mixed connectivity and mixed fault diameter of a graph, that generalize connectivity and fault diameter with respect to one type of failures. In some cases we improve results of one type of failures on Cartesian graph products and bundles

Edge, vertex and mixed fault diameters of Cartesian graph products and bundels

V disertaciji raziskujemo povezanost in okvarne premere kartezičnih grafovskih svežnjev in kartezičnih produktov. Vpeljemo mešano povezanost in mešani okvarni premer grafa, ki posplošujeta povezanosti in okvarna premera definirana glede na eno vrsto okvarjenih elementov. Nekatere rezultate na kartezičnih grafovskih svežnjih in produktih glede na eno vrsto okvarjenih elementov posplošimo in v določenih primerih tudi izboljšamo.In dissertation we study connectivity and fault diameters of Cartesian graph products and bundles. We define mixed connectivity and mixed fault diameter of a graph, that generalize connectivity and fault diameter with respect to one type of failures. In some cases we improve results of one type of failures on Cartesian graph products and bundles