The bondage number of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph a domination number greater than the domination number of G. In this paper, we prove that ...The bondage number of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph a domination number greater than the domination number of G. In this paper, we prove that for a 1-planar graph G.展开更多
The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, ...The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, r f(G) , is defined to be the minimum cardinality of a set of edges which when added to G results in a graph G′ satisfying γ f(G′)< γ f(G) . G.S.Domke and R.C.Laskar initiated the study of them and gave exact values of b f(G) and r f(G) for some classes of graphs. Exact values of b f(G) and r f(G) for complete multipartite graphs are given and some results are extended.展开更多
Jessica, the daughter of Shylock in The Merchant of Venice, has often been hailed as a free woman after she disentangles herself from the bondage of her patriarchal father. However, this paper argues that she is still...Jessica, the daughter of Shylock in The Merchant of Venice, has often been hailed as a free woman after she disentangles herself from the bondage of her patriarchal father. However, this paper argues that she is still prejudiced against by her new friends because she is considered to be a Jewess by blood. So her flight from her father is not an escape from bondage but a plunge into another kind of bondage.展开更多
The bondage number b(G) of a graph G is defined to be the cardinality of a smallest set E of edges for which λ(G-E) 】 λ(G). In this paper,we get the bondage number of P2×P.
Bonded labor,also known as debt slavery,has emerged as the predominant form of debt bondage in numerous developing economies.In the context of Pakistan,despite its legal prohibition,the practice is supported by an inf...Bonded labor,also known as debt slavery,has emerged as the predominant form of debt bondage in numerous developing economies.In the context of Pakistan,despite its legal prohibition,the practice is supported by an influential segment of society.This phenomenon is deeply rooted in a matrix of governmental failure,autocratic governance structures,pervasive social inequalities,and the systemic marginalization of specific communities.This study uses a distinctive dataset to scrutinize the statistical dynamics of bonded labor in Pakistan.Utilizing the Cox proportional hazards model,we investigate the likelihood of individuals resorting to debt bondage in Pakistan.Our analysis identifies a constellation of critical factors intimately linked with the profiles and household backgrounds of individuals entangled in debt bondage.These determinants encompass inherited familial wealth,acute health crises,unforeseeable catastrophic occurrences,household income levels,educational attainment,the burden of dependents,and the financial implications of dowry obligations.Furthermore,our research elucidates a significant association between the economic marginalization within labor markets and the wage disparities underscored and exacerbated by debt bondage contracts.展开更多
The bondage number b（G） of number of edges whose removal from G number greater than that of G. Denote a nonempty graph G is the smallest results in a graph with domination Pn × Pm the Cartesian product of two p...The bondage number b（G） of number of edges whose removal from G number greater than that of G. Denote a nonempty graph G is the smallest results in a graph with domination Pn × Pm the Cartesian product of two paths Pn and Pm. This paper determines the exact values of b（Pn × P2）, b（Pn × P3）, and b（Pn × P4） for n ≥ 2.展开更多
A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V （G） S is also adjacent to a vertex in V （G） S. Th...A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V （G） S is also adjacent to a vertex in V （G） S. The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G. In this paper we initiate the study of total restrained bondage in graphs. The total restrained bondage number in a graph G with no isolated vertex, is the minimum cardinality of a subset of edges E such that G E has no isolated vertex and the total restrained domination number of G E is greater than the total restrained domination number of G. We obtain several properties, exact values and bounds for the total restrained bondage number of a graph.展开更多
The bondage number b（G） of a graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with a domination number greater than that of G. In this paper, we obtain the exact value of ...The bondage number b（G） of a graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with a domination number greater than that of G. In this paper, we obtain the exact value of the bondage number of the strong product of two paths. That is, for any two positive integers ra ≥ 2 and n ≥ 2, b（Pm × Pn） = 7 - r（m） - r（n） if （r（m）,r（n）） = （1, 1） or （3,3）, 6 - r（m） - r（n） otherwise, where r（t） is a function of positive integer t, defined as r（t） = 1 if t ≡ 1 （mod 3）, r（t） = 2 if t ≡2 （mod 3）, and r（t） = 3 if t ≡0 （mod 3）.展开更多
China’s pioneer project of reforming its hukou system starts All non-urban workers in Chengdu,southwest China’s Sichuan Province,were covered by social security on April1.The action was regarded as one of the most i...China’s pioneer project of reforming its hukou system starts All non-urban workers in Chengdu,southwest China’s Sichuan Province,were covered by social security on April1.The action was regarded as one of the most important measures taken by the Chengdu Municipal Government to reform its household registration,or hukou,system.展开更多
文摘The bondage number of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph a domination number greater than the domination number of G. In this paper, we prove that for a 1-planar graph G.
文摘The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, r f(G) , is defined to be the minimum cardinality of a set of edges which when added to G results in a graph G′ satisfying γ f(G′)< γ f(G) . G.S.Domke and R.C.Laskar initiated the study of them and gave exact values of b f(G) and r f(G) for some classes of graphs. Exact values of b f(G) and r f(G) for complete multipartite graphs are given and some results are extended.
文摘Jessica, the daughter of Shylock in The Merchant of Venice, has often been hailed as a free woman after she disentangles herself from the bondage of her patriarchal father. However, this paper argues that she is still prejudiced against by her new friends because she is considered to be a Jewess by blood. So her flight from her father is not an escape from bondage but a plunge into another kind of bondage.
文摘The bondage number b(G) of a graph G is defined to be the cardinality of a smallest set E of edges for which λ(G-E) 】 λ(G). In this paper,we get the bondage number of P2×P.
文摘Bonded labor,also known as debt slavery,has emerged as the predominant form of debt bondage in numerous developing economies.In the context of Pakistan,despite its legal prohibition,the practice is supported by an influential segment of society.This phenomenon is deeply rooted in a matrix of governmental failure,autocratic governance structures,pervasive social inequalities,and the systemic marginalization of specific communities.This study uses a distinctive dataset to scrutinize the statistical dynamics of bonded labor in Pakistan.Utilizing the Cox proportional hazards model,we investigate the likelihood of individuals resorting to debt bondage in Pakistan.Our analysis identifies a constellation of critical factors intimately linked with the profiles and household backgrounds of individuals entangled in debt bondage.These determinants encompass inherited familial wealth,acute health crises,unforeseeable catastrophic occurrences,household income levels,educational attainment,the burden of dependents,and the financial implications of dowry obligations.Furthermore,our research elucidates a significant association between the economic marginalization within labor markets and the wage disparities underscored and exacerbated by debt bondage contracts.
文摘The bondage number b（G） of number of edges whose removal from G number greater than that of G. Denote a nonempty graph G is the smallest results in a graph with domination Pn × Pm the Cartesian product of two paths Pn and Pm. This paper determines the exact values of b（Pn × P2）, b（Pn × P3）, and b（Pn × P4） for n ≥ 2.
文摘A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V （G） S is also adjacent to a vertex in V （G） S. The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G. In this paper we initiate the study of total restrained bondage in graphs. The total restrained bondage number in a graph G with no isolated vertex, is the minimum cardinality of a subset of edges E such that G E has no isolated vertex and the total restrained domination number of G E is greater than the total restrained domination number of G. We obtain several properties, exact values and bounds for the total restrained bondage number of a graph.
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant No. 61073046）.
文摘The bondage number b（G） of a graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with a domination number greater than that of G. In this paper, we obtain the exact value of the bondage number of the strong product of two paths. That is, for any two positive integers ra ≥ 2 and n ≥ 2, b（Pm × Pn） = 7 - r（m） - r（n） if （r（m）,r（n）） = （1, 1） or （3,3）, 6 - r（m） - r（n） otherwise, where r（t） is a function of positive integer t, defined as r（t） = 1 if t ≡ 1 （mod 3）, r（t） = 2 if t ≡2 （mod 3）, and r（t） = 3 if t ≡0 （mod 3）.
文摘China’s pioneer project of reforming its hukou system starts All non-urban workers in Chengdu,southwest China’s Sichuan Province,were covered by social security on April1.The action was regarded as one of the most important measures taken by the Chengdu Municipal Government to reform its household registration,or hukou,system.
