Graph coloring has interesting real life applications in optimization and network design. In this paper some new results on the acyclic-edge coloring, f-edge coloring, g-edge cover coloring, （g, f）-coloring and equi...Graph coloring has interesting real life applications in optimization and network design. In this paper some new results on the acyclic-edge coloring, f-edge coloring, g-edge cover coloring, （g, f）-coloring and equitable edge-coloring of graphs are introduced. In particular, some new results related to the above colorings obtained by the authors are given. Some new problems and conjectures are presented.展开更多
The minimum number of total independent partition sets of V ∪ E of graph G（V,E） is called the total chromatic number of G denoted by χt（G）. If the difference of the numbers of any two total independent partition...The minimum number of total independent partition sets of V ∪ E of graph G（V,E） is called the total chromatic number of G denoted by χt（G）. If the difference of the numbers of any two total independent partition sets of V ∪ E is no more than one＇, then the minimum number of total independent partition sets of V ∪ E is called the equitable total chromatic number of G, denoted by χet（G）. In this paper, we obtain the equitable total chromatic number of the join graph of fan and wheel with the same order.展开更多
The total chromatic number χt(G) of a graph G(V,E) is the minimum number of total independent partition sets of V E, satisfying that any two sets have no common element. If the difference of the numbers of any two to...The total chromatic number χt(G) of a graph G(V,E) is the minimum number of total independent partition sets of V E, satisfying that any two sets have no common element. If the difference of the numbers of any two total independent partition sets of V E is no more than one, then the minimum number of total independent partition sets of V E is called the equitable total chromatic number of G, denoted by χet(G). In this paper, we have obtained the equitable total chromatic number of Wm Kn, Fm Kn and Sm Kn whi...展开更多
It has been known that determining the exact value of vertex distinguishing edge index X ＇8（G） of a graph G is difficult, even for simple classes of graphs such as paths, cycles, bipartite complete graphs, complete...It has been known that determining the exact value of vertex distinguishing edge index X ＇8（G） of a graph G is difficult, even for simple classes of graphs such as paths, cycles, bipartite complete graphs, complete, graphs, and graphs with maximum degree 2. Let rid（G） denote the number of vertices of degree d in G, and let X＇es（G） be the equitable vertex distinguishing edge index of G. We show that a tree T holds nl （T） ≤ X ＇s （T） ≤ n1 （T） ＋ 1 and X＇s（T） = X＇es（T） if T satisfies one of the following conditions （i） n2（T） ≤△（T） or （ii） there exists a constant c with respect to 0 〈 c 〈 1 such that n2（T） △ cn1（T） and ∑3 ≤d≤△（T）nd（T） ≤ （1 - c）n1（T） ＋ 1.展开更多
Let G（V, E） be a graph. A k-adjacent vertex-distinguishing equatable edge coloring of G, k-AVEEC for short, is a proper edge coloring f if （1） C（u）≠C（v） for uv ∈ E（G）, where C（u） = {f（uv）｜uv ∈ E}, a...Let G（V, E） be a graph. A k-adjacent vertex-distinguishing equatable edge coloring of G, k-AVEEC for short, is a proper edge coloring f if （1） C（u）≠C（v） for uv ∈ E（G）, where C（u） = {f（uv）｜uv ∈ E}, and （2） for any i, j = 1, 2,… k, we have ｜｜Ei｜ ｜Ej｜｜ ≤ 1, where Ei = {e｜e ∈ E（G） and f（e） = i}. χáve （G） = min{k｜ there exists a k-AVEEC of G} is called the adjacent vertex-distinguishing equitable edge chromatic number of G. In this paper, we obtain the χ áve （G） of some special graphs and present a conjecture.展开更多
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 10871119, 10971121 and Quality Control Standards on Undergraduate Medical Education under Grant No. 200804220001.
文摘Graph coloring has interesting real life applications in optimization and network design. In this paper some new results on the acyclic-edge coloring, f-edge coloring, g-edge cover coloring, （g, f）-coloring and equitable edge-coloring of graphs are introduced. In particular, some new results related to the above colorings obtained by the authors are given. Some new problems and conjectures are presented.
基金Supported by the National Natural Science Foundation of China(No.10771091)
文摘The minimum number of total independent partition sets of V ∪ E of graph G（V,E） is called the total chromatic number of G denoted by χt（G）. If the difference of the numbers of any two total independent partition sets of V ∪ E is no more than one＇, then the minimum number of total independent partition sets of V ∪ E is called the equitable total chromatic number of G, denoted by χet（G）. In this paper, we obtain the equitable total chromatic number of the join graph of fan and wheel with the same order.
基金the National Natural Science Foundation of China (No.10771091)
文摘The total chromatic number χt(G) of a graph G(V,E) is the minimum number of total independent partition sets of V E, satisfying that any two sets have no common element. If the difference of the numbers of any two total independent partition sets of V E is no more than one, then the minimum number of total independent partition sets of V E is called the equitable total chromatic number of G, denoted by χet(G). In this paper, we have obtained the equitable total chromatic number of Wm Kn, Fm Kn and Sm Kn whi...
基金supported by the National Natural Science Foundation of China (61163054),supported by the National Natural Science Foundation of China (61163037)
文摘It has been known that determining the exact value of vertex distinguishing edge index X ＇8（G） of a graph G is difficult, even for simple classes of graphs such as paths, cycles, bipartite complete graphs, complete, graphs, and graphs with maximum degree 2. Let rid（G） denote the number of vertices of degree d in G, and let X＇es（G） be the equitable vertex distinguishing edge index of G. We show that a tree T holds nl （T） ≤ X ＇s （T） ≤ n1 （T） ＋ 1 and X＇s（T） = X＇es（T） if T satisfies one of the following conditions （i） n2（T） ≤△（T） or （ii） there exists a constant c with respect to 0 〈 c 〈 1 such that n2（T） △ cn1（T） and ∑3 ≤d≤△（T）nd（T） ≤ （1 - c）n1（T） ＋ 1.
基金Supported by the National Natural Science Foundation of China(No.10771091No.61163010)Ningxia University Science Research Foundation(No.(E)ndzr09-15)
文摘Let G（V, E） be a graph. A k-adjacent vertex-distinguishing equatable edge coloring of G, k-AVEEC for short, is a proper edge coloring f if （1） C（u）≠C（v） for uv ∈ E（G）, where C（u） = {f（uv）｜uv ∈ E}, and （2） for any i, j = 1, 2,… k, we have ｜｜Ei｜ ｜Ej｜｜ ≤ 1, where Ei = {e｜e ∈ E（G） and f（e） = i}. χáve （G） = min{k｜ there exists a k-AVEEC of G} is called the adjacent vertex-distinguishing equitable edge chromatic number of G. In this paper, we obtain the χ áve （G） of some special graphs and present a conjecture.
