设图 G=(V,E).一子集 D■V,若对每一个 X■V-D,都存在一个非空子集合Y■D,使得由 X∪Y所导出的子图<X∪Y>连通,则称 D 为 G 的一个集控制集(sd-集).G 的集控制数γ.(G)是 G 的一个集控制集的最小基数.本文给出了集控制集的一个充...设图 G=(V,E).一子集 D■V,若对每一个 X■V-D,都存在一个非空子集合Y■D,使得由 X∪Y所导出的子图<X∪Y>连通,则称 D 为 G 的一个集控制集(sd-集).G 的集控制数γ.(G)是 G 的一个集控制集的最小基数.本文给出了集控制集的一个充要条件,并讨论了生成子图与补图的集控制数.展开更多
In this research paper, an attempt has been made to come across the effect of distance between double glazing on the efficiency of a solar thermal collector. Experiments were carded out on an active solar energy demon...In this research paper, an attempt has been made to come across the effect of distance between double glazing on the efficiency of a solar thermal collector. Experiments were carded out on an active solar energy demonstration system （ET 200）. Commercial glass pane of 3 mm thick having the same dimensions as that of the apparatus was placed above the collector at a distance of 2 cm, 4 cm and 6 cm. Tests were done with and without the added glass. Experiments were performed for double glazing with two positions of the light meter. In one position, it was placed in the middle of the collector surface. While, in the other one, the light meter was placed in the middle of the added glass. To study the effect of double glazing on the performance of the solar collector ET 200, the correct position of the light meter was to place it exactly in the middle of the additional pane under the lamp. Double glazing does not enhance the performance of the solar collector because of the high resistance of the system glass air glass. The efficiency of double glazing solar collector decreases with the increasing the distance of the two separated glasses.展开更多
A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G, such that every vertex of G is dominated by at least two vertices of D. The do...A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G, such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G = （V, E）, a subset D C V（G） is a 2-dominating set if every vertex of V（G） ／ D has at least two neighbors in D, while it is a 2-outer-independent dominating set of G if additionally the set V（G）／D is independent. The 2-outer-independent domination number of G is the minimum cardinality of a 2-outer-independent dominating set of G. This paper characterizes all trees with the double domination number equal to the 2-outer-independent domination number plus one.展开更多
A 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D.A total outer-independent dominating set of a graph G is a set D of vertices of G such that ...A 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D.A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D,and the set V(G)\D is independent.The 2-domination(total outer-independent domination,respectively)number of a graph G is the minimum cardinality of a 2-dominating(total outer-independent dominating,respectively)set of G.We investigate the ratio between2-domination and total outer-independent domination numbers of trees.展开更多
文摘设图 G=(V,E).一子集 D■V,若对每一个 X■V-D,都存在一个非空子集合Y■D,使得由 X∪Y所导出的子图<X∪Y>连通,则称 D 为 G 的一个集控制集(sd-集).G 的集控制数γ.(G)是 G 的一个集控制集的最小基数.本文给出了集控制集的一个充要条件,并讨论了生成子图与补图的集控制数.
文摘In this research paper, an attempt has been made to come across the effect of distance between double glazing on the efficiency of a solar thermal collector. Experiments were carded out on an active solar energy demonstration system （ET 200）. Commercial glass pane of 3 mm thick having the same dimensions as that of the apparatus was placed above the collector at a distance of 2 cm, 4 cm and 6 cm. Tests were done with and without the added glass. Experiments were performed for double glazing with two positions of the light meter. In one position, it was placed in the middle of the collector surface. While, in the other one, the light meter was placed in the middle of the added glass. To study the effect of double glazing on the performance of the solar collector ET 200, the correct position of the light meter was to place it exactly in the middle of the additional pane under the lamp. Double glazing does not enhance the performance of the solar collector because of the high resistance of the system glass air glass. The efficiency of double glazing solar collector decreases with the increasing the distance of the two separated glasses.
文摘A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G, such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G = （V, E）, a subset D C V（G） is a 2-dominating set if every vertex of V（G） ／ D has at least two neighbors in D, while it is a 2-outer-independent dominating set of G if additionally the set V（G）／D is independent. The 2-outer-independent domination number of G is the minimum cardinality of a 2-outer-independent dominating set of G. This paper characterizes all trees with the double domination number equal to the 2-outer-independent domination number plus one.
基金the Polish Ministry of Science and Higher Education grand IP/2012/038972
文摘A 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D.A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D,and the set V(G)\D is independent.The 2-domination(total outer-independent domination,respectively)number of a graph G is the minimum cardinality of a 2-dominating(total outer-independent dominating,respectively)set of G.We investigate the ratio between2-domination and total outer-independent domination numbers of trees.
