Co/Sb multilayer shows the theoretical reflectance of 62% at a photoenergy of 528 eV and the grazing angle of 10.3, but the measured reflectance is very low, which is considered to result from the low energy resolutio...
ALL graphs appearing in this note are simple. A graph with p vertices and q edges will becalled a (p, q )-graph. The maximum degree of G is denoted by Δ(G).Let n≥2 be an integer. The n-edge chromatic number X_n (G) ...
Project supported by the National Natural Science Foundation of China and Natural Science Fund of Gansu Province, China.
Let G(V, E) be a simple graph, f: C→V(G) be an injection, and all vertices on the path whose length is no longer than n be assigned different colors, where C is a color set. Then f is called an n-coloring of G. If |C...
The graphs considered here are finite and contain no loops nor multiple edges. Let G be such a graph, M(G; W) be its matching polynomial defined by Farrell in 1979, P(G; λ) be its chromatic polynomial. A graph G is m...
This research was supported by the National Natural Science Foundation of China.
On chromatic enumeration, the first paper which is for rooted planar triangulations was published in 1973. Ten years later, the author generalized the theory into that for rooted nonseparable maps. Very recently, the ...
We consider the colouring of both the vertices and edges. The total chromatic number X_T(G) of a graph G is the minimum number of colours required for colouring the elements (i. e. vertices and edges) of G so that the...
Let P denote the set of all prime numbers, and D(?) P. Let G(Z, D) denote the graph with the integers as its vertex set and the edges between those pairs of integers with absolute difference in the set D. Eggleton, Er...
On chromatic sums, W. T. Tutte published the first paper in 1973 for rooted planar triangulations. In 1984, the author discussed the problem for more general cases of rooted nonseparable planar maps. This note provide...