Motivated by work of Erdős, Ota determined the maximum size g(n,k) a k-connected nonhamiltonian graph order n in 1995. But for some pairs n,k, is not attained connectivity k. For example, g(15,3)=77 unique 7, 3. In this paper we obtain more precise information determining and k, extremal graphs. Consequently solve corresponding problem nontraceable

The atom-bond connectivity (ABC) index, introduced by Estrada et al. in 1998, displays an excellent correlation with the formation heat of alkanes. We give upper bounds for this graph invariant using the number of vertices, the number of edges, the Randić connectivity indices, and the first Zagreb index. We determine the unique tree with the maximum ABC index among trees with given numbers of v...

BACKGROUND It has been previously shown that loss of consciousness is associated with a breakdown of dominating fronto-parietal feedback connectivity as assessed by electroencephalogram (EEG) recordings. Structure and strength of network connectivity may change over time. Aim of the current study is to investigate cortico-cortical connectivity at different time intervals during consciousness an...

We first consider the Steiner edge connectivity problem on an unweighted undirected or Eulerian directed graph with n vertices and m edges. This problem involves finding the edge connectivity of a specified subset S of vertices, i.e. the cardinality of the minimum cut in the graph that separates the vertices in S into two parts. We give a deterministic algorithm for this problem that runs in Õ(...

Need for high speed internet connectivity has lead to a substantial research in switching systems. Buffered crossbar switches have received a lot of attention from both research and industrial communities due of its flexibility and scalability. Designing a scheduling algorithm for buffered crossbar switches without starvation is a major challenge as of now. In this paper, we proposed a Delay ba...

An optimum sensor node placement mechanism for Wireless Sensor Network (WSN) is desirable in ensuring the location of sensor nodes that offers maximum coverage and connectivity with minimum energy consumption. This paper proposes a sensor node placement algorithm that utilizes a new biologically inspired optimization algorithm that imitates the behaviour of territorial predators in marking thei...

For a graph G, let χ(G) and λ(G) denote the chromatic number of G and the maximum local edge connectivity of G, respectively. A result of Dirac implies that every graph G satisfies χ(G) 6 λ(G) + 1. In this paper we characterize the graphs G for which χ(G) = λ(G) + 1. The case λ(G) = 3 was already solved by Aboulker, Brettell, Havet, Marx, and Trotignon. We show that a graph G with λ(G) = k > 4 ...

In this note, we show that one of the arguments used by Moazzami for computing the tenacity of the third Harary graph is wrong and then improve the proof. © 2014 Published by Elsevier B.V.

This study addresses the possible significance of trabecular connectivity for the mechanical quality of cancellous bone. A total of 141 cubic trabecular bone specimens collected from autopsy material from 56 individuals without any known bone or metastatic diseases were used. Age variation was in the range of 14-91 years and a wide range of trabecular architecture was found. Each specimen was t...