5,054 research outputs found

    Rainbow Connection Numbers of WK-Recursive Networks and WK-Recursive Pyramids

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    An edge coloring of a graph G results in G being rainbow connected when every pair of vertices is linked by a rainbow path. Such a path is defined as one where each edge possesses a distinct color. A rainbow coloring refers to an edge coloring that guarantees the rainbow connectedness of G. The rainbow connection number of G represents the smallest quantity of colors required to achieve rainbow connectedness under a rainbow coloring scheme. Wang and Hsu (ICICM 2019: 75–79) provided upper bounds on the size of the rainbow connection numbers in WK-recursive networks WKd,t and WK-recursive pyramids WKPd,n. In this paper, we revise their results and determine the exact values of the rainbow connection numbers of WKd,2 for d=3 and 4. The rainbow connection numbers of WKd,2 are bounded between 4 and ⌊d2⌋+2 for d>4. In addition to our previous findings, we further investigate and determine upper bounds for the size of the rainbow connection numbers of WKPd,n. This involves analyzing various aspects of the graph structure and exploring potential limitations on the rainbow connection numbers. By establishing these upper bounds, we gain deeper insights into the potential range and constraints of the rainbow connection numbers within the given context

    Sulfur forming an isoelectronic center in zinc telluride thin films

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    ZnTe1-xSx epitaxial layers grown on GaAs by molecular-beam epitaxy were studied by photoluminescence (PL) as a function of temperatures, excitation powers, and hydrostatic pressures. A sulfur-related emission peak, labeled as P-2, is identified as a deep-level emission by hydrostatic-pressure PL measurement. This indicates that sulfur atoms form isoelectronic centers in a ZnTe matrix. The results qualitatively agree with the theoretical prediction and show experimental evidence of isoelectronic S in ZnTe. A model is proposed to explain the emission mechanisms in the ZnTe1-xSx system with small x values
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