The study of minus paired domination of a graph G=(V,E) is initiated. Let SV be any paired dominating set of G , a minus paired dominating function is a function of the form f∶V→{-1,0,1} such that ...The study of minus paired domination of a graph G=(V,E) is initiated. Let SV be any paired dominating set of G , a minus paired dominating function is a function of the form f∶V→{-1,0,1} such that f(v)= 1 for v∈S, f(v)≤0 for v∈V-S , and f(N)≥1 for all v∈V . The weight of a minus paired dominating function f is w(f)=∑f(v) , over all vertices v∈V . The minus paired domination number of a graph G is γ - p( G )=min{ w(f)|f is a minus paired dominating function of G }. On the basis of the minus paired domination number of a graph G defined, some of its properties are discussed.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 γ f(G) and γ~t f(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of P n...Let γ f(G) and γ~t f(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of P n×P m (grid graph) with small n and m . But for large n and m , it is difficult to decide the exact fractional domination number. Motivated by this, nearly sharp upper and lower bounds are given to the fractional domination number of grid graphs. Furthermore, upper and lower bounds on the fractional total domination number of strong direct product of graphs are given.展开更多
文摘The study of minus paired domination of a graph G=(V,E) is initiated. Let SV be any paired dominating set of G , a minus paired dominating function is a function of the form f∶V→{-1,0,1} such that f(v)= 1 for v∈S, f(v)≤0 for v∈V-S , and f(N)≥1 for all v∈V . The weight of a minus paired dominating function f is w(f)=∑f(v) , over all vertices v∈V . The minus paired domination number of a graph G is γ - p( G )=min{ w(f)|f is a minus paired dominating function of G }. On the basis of the minus paired domination number of a graph G defined, some of its properties are discussed.
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.
文摘Let γ f(G) and γ~t f(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of P n×P m (grid graph) with small n and m . But for large n and m , it is difficult to decide the exact fractional domination number. Motivated by this, nearly sharp upper and lower bounds are given to the fractional domination number of grid graphs. Furthermore, upper and lower bounds on the fractional total domination number of strong direct product of graphs are given.
