In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.

In this paper we present explicit formulas for the eccentric connectivity index of three classes of chain hexagonal cacti. Further, it is shown that the extremal chain hexagonal cacti with respect to the eccentric connectivity index belong to one of the considered types. Some open problems and possible directions of further research are mentioned in the concluding section.

In this paper,we propose a distributedmulti-sectormulti-range (MSMR) control algorithm for supporting self-organizing wireless networks. The algorithm enables us to reduce the unnecessary coverage with fine-tuned range control and also to increase the network-wide capacity with enhanced spatial reusability. The proposed algorithm discovers neighboring nodes within the maximum transmission range...

Most demersal fishes undergo a dispersal phase as larvae, which strongly influences the connectivity among adult populations and, consequently, their genetic structure and replenishment opportunities. Because this phase is difficult to observe directly, it is frequently simulated through numerical models, most of which consider larvae as passive or only vertically migrating. However, in several...

While the effect of habitat connectivity on local and regional diversity has been analysed in a number of studies, time-dependent dynamics in metacommunities have received comparatively little consideration. When local patches of a metacommunity are identical in environmental conditions but differ in initial community composition, dispersal among patches may result in homogenization of local co...

A graph G = (V,E) is called l-mixed p-connected if G−S−L is connected for all pairs S, L with S ⊆ V , L ⊆ E, and l|S|+ |L| < p. This notion is a common generalisation of m-vertex-connectivity (l = 1, p = m) and m-edge-connectivity (l ≥ m, p = m). If p = kl then we obtain (k, l)-connectivity, introduced earlier by Kaneko and Ota, as a special case. We show that by using maximum adjacency orderin...

We investigate the bounds on algebraic connectivity of graphs subject to constraints on the number of edges, vertices, and topology. We show that the algebraic connectivity for any tree on n vertices and with maximum degree d is bounded above by 2 (d− 2) 1 n + O ( lnn n2 ) . We then investigate upper bounds on algebraic connectivity for cubic graphs. We show that algebraic connectivity of a cub...

In Survivable Network problems (a.k.a. Survivable Network Design Problem – SNDP) we are given a graph with costs/weights on edges and/or nodes and prescribed connectivity requirements/demands. Among the subgraphs of G that satisfy the requirements, we seek to find one of minimum cost. Formally, the problem is defined as follows. Given a graph G = (V,E) and Q ⊆ V , the Q-connectivity λQG(uv) of ...

In the vertex connectivity survivable network design problem we are given an undirected graph G = (V,E) and connectivity requirement r(u, v) for each pair of vertices u, v ∈ V .We are also given a cost function on the set of edges. Our goal is to find the minimum cost subset of edges such that for every pair (u, v) of vertices we have r(u, v) vertex disjoint paths in the graph induced by the ch...