A k-total coloring of a graph G is a mapping φ： V（G） U E（G） → {1, 2,..., k} such that no two adjacent or incident elements in V（G） U E（G） receive the same color. Let f（v） denote the sum of the color on th...A k-total coloring of a graph G is a mapping φ： V（G） U E（G） → {1, 2,..., k} such that no two adjacent or incident elements in V（G） U E（G） receive the same color. Let f（v） denote the sum of the color on the vertex v and the colors on all edges incident with v. We say that ~ is a k-neighbor sum distinguishing total coloring of G if f（u） ≠ f（v） for each edge uv C E（G）. Denote X＂ （G） the smallest value k in such a coloring of G. Pilgniak and Wo/niak conjectured that for any simple graph with maximum degree △（G）, X＂（G） ≤ 3. In this paper, by using the famous Combinatorial Nullstellensatz, we prove that for Ka-minor free graph G with △（G） ≥ 5, X＂（G） = △（G） ＋ 1 if G contains no two adjacent A-vertices, otherwise, X＂（G） = △（G） ＋ 2.展开更多
Graphitic carbon nitride(g-C3N4)has attracted considerable attention due to its special structure and properties,such as its good chemical and thermal stability under ambient conditions,low cost and non-toxicity,and f...Graphitic carbon nitride(g-C3N4)has attracted considerable attention due to its special structure and properties,such as its good chemical and thermal stability under ambient conditions,low cost and non-toxicity,and facile synthesis.Recently,g-C3N4-based sensors have been demonstrated to be of high interests in the areas of sensing due to the unique optical,electronic and catalytic properties of g-C3N4.This review focuses on the most salient advances in luminescent sensors based on g-C3N4,chemiluminescence,cataluminescence and electrochemiluminescence methods are discussed.This review provides valuable information for researchers of related areas and thus may inspire the development of more practical and effective approaches for designing two-dimensional(2D)nanomaterial-assisted luminescent sensors.展开更多
文摘A k-total coloring of a graph G is a mapping φ： V（G） U E（G） → {1, 2,..., k} such that no two adjacent or incident elements in V（G） U E（G） receive the same color. Let f（v） denote the sum of the color on the vertex v and the colors on all edges incident with v. We say that ~ is a k-neighbor sum distinguishing total coloring of G if f（u） ≠ f（v） for each edge uv C E（G）. Denote X＂ （G） the smallest value k in such a coloring of G. Pilgniak and Wo/niak conjectured that for any simple graph with maximum degree △（G）, X＂（G） ≤ 3. In this paper, by using the famous Combinatorial Nullstellensatz, we prove that for Ka-minor free graph G with △（G） ≥ 5, X＂（G） = △（G） ＋ 1 if G contains no two adjacent A-vertices, otherwise, X＂（G） = △（G） ＋ 2.
基金the National Natural Science Foundation of China[nos.21405107 and 21375089].
文摘Graphitic carbon nitride(g-C3N4)has attracted considerable attention due to its special structure and properties,such as its good chemical and thermal stability under ambient conditions,low cost and non-toxicity,and facile synthesis.Recently,g-C3N4-based sensors have been demonstrated to be of high interests in the areas of sensing due to the unique optical,electronic and catalytic properties of g-C3N4.This review focuses on the most salient advances in luminescent sensors based on g-C3N4,chemiluminescence,cataluminescence and electrochemiluminescence methods are discussed.This review provides valuable information for researchers of related areas and thus may inspire the development of more practical and effective approaches for designing two-dimensional(2D)nanomaterial-assisted luminescent sensors.
