The objective of the thesis is to discuss edge-connectivity and related connectivity conceptsin the context of undirected and directed hypergraphs. In particular, we focus on k-edge-connectivity and (k, l)-partition-connectivity of hypergraphs, and (k, l)-edge-connectivityof directed hypergraphs. A strong emphasis is placed on the role of submodularity in thestructural aspects o...

in this paper, a new molecular-structure descriptor, the general sum–connectivity co–index  is considered, which generalizes the first zagreb co–index and the general sum–connectivity index of graph theory. we mainly explore the lower and upper bounds in termsof the order and size for this new invariant. additionally, the nordhaus–gaddum–type resultis also represented.

The edge tenacity Te(G) of a graph G is dened as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split...

In this paper, the concept of σ−connectivity in L−topological spaces is introduced. Some properties for σ−connectivity in L−topological spaces are characterized systematically. The famous K.Fan’s Theorem holds for σ−connectivity in L−topological spaces. Mathematics Subject Classification: 54A40

The thermal reaction norms of 4 closely related intertidal Nacellid limpets, Antarctic (Nacella concinna), New Zealand (Cellana ornata), Australia (C. tramoserica) and Singapore (C. radiata), were compared across environments with different temperature magnitude, variability and predictability, to test their relative vulnerability to different scales of climate warming. Lethal limits were measu...