A graph is said to be cyclic k-edge-connected, if at least k edges must be removed to disconnect it into two components, each containing a cycle. Such a set of k edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single k-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all ...

A size- and shape-selective synthesis of pentagonally twinned silver icosahedral nanoparticles (AgIhNPs), one of the five platonic solid morphologies, has been developed by integrating three key factors: nuclei templating by copper, photochemical development using violet LED light and chemical oxidative etching. The presence of copper is essential for AgIhNP shape selection via the promotion of...

In this paper, medical diagnosis concerning isolated systolic hypertension and a study on implication operators is introduced, but fuzzy pentagonal number matrix concepts developed to give numerical example graphical representation are also established.

In this paper, we provide some recurrence relations connecting restricted partition functions and mock theta functions. Elementary manipulations are used including Jacobi triple product identity, Euler’s pentagonal number theorem, Ramanujan’s for finding the relations.

Three indium-oxide organic frameworks, In(2)O(1,3-BDC)(2), 1; In(OH)(2,6-NDC)(H(2)O), 2; and In(OH)(2,7-NDC)(H(2)O), 3 (BDC = benzene dicarboxylic acid and NDC = naphthalene dicarboxylic acid), were synthesized and characterized by thermogravimetric analysis, infrared spectroscopy, and single-crystal X-ray diffraction. Previously, we reported the structure of In(OH)(1,4-BDC).(0.75H(2)BDC), 0, w...

The purpose of this research is to investigate a novel three-stage flow shop scheduling problem with an ambiguous processing time. uncertain information characterized by Pentagonal fuzzy numbers. To solve the problem, in paper, two different strategies are proposed; one relies on idea ranking function, and other close interval approximation pentagonal number. For persons that need be more speci...