The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs...The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs G with ds'(G) = q – Δ'(G) + 1 and investigate well-edge dominated graphs. We further define γ'–-critical, γ'+-critical, ds'–-critical, ds'+-critical edges and study some of their properties.展开更多
Let be a simple graph with vertex set and edge set . Let have at least vertices of degree at least , where and are positive integers. A function is said to be a signed -edge cover of if for at least vertices of , wher...Let be a simple graph with vertex set and edge set . Let have at least vertices of degree at least , where and are positive integers. A function is said to be a signed -edge cover of if for at least vertices of , where . The value , taking over all signed -edge covers of is called the signed -edge cover number of and denoted by . In this paper we give some bounds on the signed -edge cover number of graphs.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The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs G with ds'(G) = q – Δ'(G) + 1 and investigate well-edge dominated graphs. We further define γ'–-critical, γ'+-critical, ds'–-critical, ds'+-critical edges and study some of their properties.
文摘Let be a simple graph with vertex set and edge set . Let have at least vertices of degree at least , where and are positive integers. A function is said to be a signed -edge cover of if for at least vertices of , where . The value , taking over all signed -edge covers of is called the signed -edge cover number of and denoted by . In this paper we give some bounds on the signed -edge cover number of graphs.
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).