the notion of strong arcs in a fuzzy graph was introduced bybhutani and rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. in mordeson and yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.in this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...

Given a k-arc-strong tournament T , we estimate the minimum number of arcs possible in a k-arc-strong spanning subdigraph of T . We give a construction which shows that for each k ≥ 2 there are tournaments T on n vertices such that every k-arc-strong spanning subdigraph of T contains at least nk+ k(k−1) 2 arcs. In fact, the tournaments in our construction have the property that every spanning s...

The notion of strong arcs in a fuzzy graph was introduced byBhutani and Rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. In Mordeson and Yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.In this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

A digraph D is strong if it contains a directed path from x to y for every choice of vertices x, y in D. We consider the problem (MSSS) of finding the minimum number of arcs in a spanning strong subdigraph of a strong digraph. It is easy to see that every strong digraph D on n vertices contains a spanning strong subdigraph on at most 2n− 2 arcs. By reformulating the MSSS problem into the equiva...

We use semi-analytic modelling of the galaxy-cluster population and its strong lensing efficiency to explore how the expected abundance of large gravitational arcs on the sky depends on σ8. Our models take all effects into account that have been shown to affect strong cluster lensing substantially, in particular cluster asymmetry, substructure, merging, and variations in the central density con...

We study outer Lipschitz geometry of real semialgebraic or, more general, definable in a polynomially bounded o-minimal structure over the reals, surface germs. In particular, any Hölder triangle is either normally embedded or contains some “abnormal” arcs. show that abnormal arcs constitute finitely many “abnormal zones” space all arcs, and investigate geometric combinatorial properties establ...