The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of the same color.An outerplane graph with independent crossings is a gra...The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of the same color.An outerplane graph with independent crossings is a graph embedded in the plane in such a way that all vertices are on the outer face and two pairs of crossing edges share no common end vertex.It is proved that every outerplane graph with independent crossings and maximum degreeΔhas strong chromatic index at most 4Δ-6 if Δ≥4,and at most 8 ifΔ≤3.Both bounds are sharp.展开更多
A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of ...A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv∈ E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by X＇Aa（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.展开更多
The electron spin resonance, transmission and reflection spectra showed that a steadily electron-type paramagnetic complex color point defect Fn center is produced by 60Co γ-ray strong dose irradiation in a single cr...The electron spin resonance, transmission and reflection spectra showed that a steadily electron-type paramagnetic complex color point defect Fn center is produced by 60Co γ-ray strong dose irradiation in a single crystal LiF. The γ-ray irradiation dose is too large to recognize any character peak of F2, F2, F2, and F3 centers in the transmission and reflection spectra of the single crystal. LiF: Fn is opaque when wavelength is shorter than about 750nm and has not refiection when wavelength is shorter than about 800nm. The Fn center has a wide ESR peak with ΔBpp of 8 millitesla and the effect g-factor is 1.998±0.002.展开更多
基金supported by the Natural Science Basic Research Plan in Shaanxi Province of China(No.2023-JC-YB-001)the National Natural Science Foundation of China(No.11871055).
文摘The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of the same color.An outerplane graph with independent crossings is a graph embedded in the plane in such a way that all vertices are on the outer face and two pairs of crossing edges share no common end vertex.It is proved that every outerplane graph with independent crossings and maximum degreeΔhas strong chromatic index at most 4Δ-6 if Δ≥4,and at most 8 ifΔ≤3.Both bounds are sharp.
基金supported by NSFC of China (No. 19871036 and No. 40301037)Faculty Research Grant,Hong Kong Baptist University
文摘A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv∈ E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by X＇Aa（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.
文摘The electron spin resonance, transmission and reflection spectra showed that a steadily electron-type paramagnetic complex color point defect Fn center is produced by 60Co γ-ray strong dose irradiation in a single crystal LiF. The γ-ray irradiation dose is too large to recognize any character peak of F2, F2, F2, and F3 centers in the transmission and reflection spectra of the single crystal. LiF: Fn is opaque when wavelength is shorter than about 750nm and has not refiection when wavelength is shorter than about 800nm. The Fn center has a wide ESR peak with ΔBpp of 8 millitesla and the effect g-factor is 1.998±0.002.
基金Support byed National Natural Science Foundation of China(10201022,10971144)Natural Science Foundationof Beijing City(1102015)Fundamental Research Funds for the Universities(2011B019)
