Domination integrity of some graph classes

Besirik, Ayse/0000-0002-3980-196XWOS: 000517221700007The stability of a communication network has a great importance in network design. There are several vulnerability measures used to determine the resistance of network to the disruption in this sense. Domination theory provides a model to measure the vulnerability of a graph network. A new vulnerability measure of domination integrity was introduced by Sundareswaran in his Ph.D. thesis (Parameters of vulnerability in graphs (2010)) and defined as DI(G) = min{|S| + m(G - S):S is an element of V(G)} where m(G - S) denotes the order of a largest component of graph G - S and S is a dominating set of G. the domination integrity of an undirected connected graph is such a measure that works on the whole graph and also the remaining components of graph after any break down. Here we determine the domination integrity of wheel graph W-1,W-n, Ladder graph L-n, S-m,S-n, Friendship graph F-n, Thorn graph of P-n and C-n which are commonly used graph models in network design

FINDING THE PATH CENTRE OF A COMMUNICATIONS NETWORK

WOS: 000273729800005The centre of a communications network is a vertex set. The distances between every vertex in the centre set and all other vertices of the network are minimal. In some cases, the centre of the network can be a path, which includes a desired number of vertices. This centre is called a path centre of the network. In this paper, we aim to find a path centre of a given network with the needed number of vertices. We give the distance measures of the network and represent an algorithm searching the path centre of the network

Comparison of total/active ghrelin levels in primary open angle glaucoma, pseudoexfoliation glaucoma and pseudoexfoliation syndrome

AIM: To investigate the levels of ghrelin (Gh), acylated ghrelin (AGh) and AGh/Gh ratio in the humor aqueous (HA) of cases with pseudoexfoliation syndrome (PXS), pseudoexfoliation glaucoma (PXG), primary open angle glaucoma (POAG) and to compare these with control subjects. METHODS: A prospective examination was made of the total Gh, and AGh levels in HA of 67 patients undergoing cataract surgery. Patients were divided into 4 groups. HA samples were aspirated at the beginning of the surgery, stored at -70oC. Gh and AGh quantification was performed with ELISA kits and the AGh/total-Gh ratios were calculated. ANOVA, Kruskal-Wallis, Chi-square and post-hoc tests were used for statistical analysis. RESULTS: Total Gh levels in HA were 189.2±45.6 pg/mL in the control group, 199.2±32.9 pg/mL in PXS, 180.6±20.9 pg/mL in PXG and 176.8±21.4 pg/mL in POAG groups (P>0.05). AGh levels in HA were 23.09±5.01 pg/mL in the control group, 24.13±5.22 pg/mL in PXS, 22.29±1.55 pg/mL in PXG and 19.69±2.93 pg/mL in POAG groups (P>0.05). The ratio of AGh/Gh was 10.3%±2.34% in the control group, 13.03%±2.58% in PXS, 12.3%±1.54% in PXG and 11.79%±1.41% in POAG groups (P=0.044). The difference between the PXS and control groups was significant (P=0.03). CONCLUSION: In spite of statistically insignificant results, the HA total Gh levels were lower than those of the control subjects but not parallel with the AGh levels in glaucoma patients. The relative increase in the AGh/Gh ratio in glaucoma cases supports the view that proportional increases of AGh might play a role in the pathogenesis of glaucoma