Let be a simple graph with vertex set V and edge set E. A function is said to be a reverse total signed vertex dominating function if for every , the sum of function values over v and the elements incident to v is les...Let be a simple graph with vertex set V and edge set E. A function is said to be a reverse total signed vertex dominating function if for every , the sum of function values over v and the elements incident to v is less than zero. In this paper, we present some upper bounds of reverse total signed vertex domination number of a graph and the exact values of reverse total signed vertex domination number of circles, paths and stars are given.展开更多
Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such ...Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such that f(N(v)) ≥1 for every vertex v∈V . The signed total domination number of a graph G equals the minimum weight of a signed total dominating function on G . In this paper, some properties of the signed total domination number of a graph G are discussed.展开更多
Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on ...Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi（x） ≤ 1 for each x ∈ V, is called a signed total dominating family （of functions） on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s（G）. The properties of the signed total domatic number dt^s（G） are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs.展开更多
Let G be a finite connected simple graph with a vertex set V（G）and an edge set E（G）. A total signed domination function of G is a function f:V（G）∪E（G）→{-1,1}.The weight of f is W（f）=∑<sub>x∈V</s...Let G be a finite connected simple graph with a vertex set V（G）and an edge set E（G）. A total signed domination function of G is a function f:V（G）∪E（G）→{-1,1}.The weight of f is W（f）=∑<sub>x∈V</sub>（G）∪E（G）)f（X）.For an element x∈V（G）∪E（G）,we define f[x]=∑<sub>y∈NT[x]</sub>f（y）.A total signed domination function of G is a function f:V（G）∪E（G）→{-1,1} such that f[x]≥1 for all x∈V（G）∪E（G）.The total signed domination numberγ<sub>s</sub><sup>*</sup>（G）of G is the minimum weight of a total signed domination function on G. In this paper,we obtain some lower bounds for the total signed domination number of a graph G and compute the exact values ofγ<sub>s</sub><sup>*</sup>（G）when G is C<sub>n</sub> and P<sub>n</sub>.展开更多
Let G = （V,E） be a graph.A function f ： E → {-1,1} is said to be a signed edge total dominating function （SETDF） of G if e ∈N（e） f（e ） ≥ 1 holds for every edge e ∈ E（G）.The signed edge total domination ...Let G = （V,E） be a graph.A function f ： E → {-1,1} is said to be a signed edge total dominating function （SETDF） of G if e ∈N（e） f（e ） ≥ 1 holds for every edge e ∈ E（G）.The signed edge total domination number γ st （G） of G is defined as γ st （G） = min{ e∈E（G） f（e）｜f is an SETDF of G}.In this paper we obtain some new lower bounds of γ st （G）.展开更多
文摘Let be a simple graph with vertex set V and edge set E. A function is said to be a reverse total signed vertex dominating function if for every , the sum of function values over v and the elements incident to v is less than zero. In this paper, we present some upper bounds of reverse total signed vertex domination number of a graph and the exact values of reverse total signed vertex domination number of circles, paths and stars are given.
文摘Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such that f(N(v)) ≥1 for every vertex v∈V . The signed total domination number of a graph G equals the minimum weight of a signed total dominating function on G . In this paper, some properties of the signed total domination number of a graph G are discussed.
基金Project supported by the National Natural Science Foundation of China （Grant No.1057117）, and the Science Foundation of Shanghai Municipal Commission of Education （Grant No.05AZ04）.
文摘Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi（x） ≤ 1 for each x ∈ V, is called a signed total dominating family （of functions） on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s（G）. The properties of the signed total domatic number dt^s（G） are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs.
基金the National Natural Science Foundation of China(Grant No.10471311)
文摘Let G be a finite connected simple graph with a vertex set V（G）and an edge set E（G）. A total signed domination function of G is a function f:V（G）∪E（G）→{-1,1}.The weight of f is W（f）=∑<sub>x∈V</sub>（G）∪E（G）)f（X）.For an element x∈V（G）∪E（G）,we define f[x]=∑<sub>y∈NT[x]</sub>f（y）.A total signed domination function of G is a function f:V（G）∪E（G）→{-1,1} such that f[x]≥1 for all x∈V（G）∪E（G）.The total signed domination numberγ<sub>s</sub><sup>*</sup>（G）of G is the minimum weight of a total signed domination function on G. In this paper,we obtain some lower bounds for the total signed domination number of a graph G and compute the exact values ofγ<sub>s</sub><sup>*</sup>（G）when G is C<sub>n</sub> and P<sub>n</sub>.
基金Supported by the National Natural Science Foundation of China (Grant No. 11061014)
文摘Let G = （V,E） be a graph.A function f ： E → {-1,1} is said to be a signed edge total dominating function （SETDF） of G if e ∈N（e） f（e ） ≥ 1 holds for every edge e ∈ E（G）.The signed edge total domination number γ st （G） of G is defined as γ st （G） = min{ e∈E（G） f（e）｜f is an SETDF of G}.In this paper we obtain some new lower bounds of γ st （G）.
