Various kinds of human disturbances on cropland are the main reasons for soil erosion and land degradation.Farming practices in mountainous areas vary greatly among cropland plots because of the heterogeneity of bioph...Various kinds of human disturbances on cropland are the main reasons for soil erosion and land degradation.Farming practices in mountainous areas vary greatly among cropland plots because of the heterogeneity of biophysical conditions and differences in farmers'management behavior.The main purpose of this paper is to develop a composite index of cropland physical disturbance intensity(CLDI)to reflect the plot-scale discrepancy of potential soil erosion in mountainous areas.The study was based on both plot survey and household interview data,collected from six typical catchments in mountainous areas of southwestern China.Four kinds of physical disturbance practices and two kinds of conservation practices during one crop rotation period were synthesized to develop the CLDI index.The rough set theory was referenced to avoid subjectivity during weight allocation.The results show that conventional tillage,deep fertilization,and manual weeding are the main causes of cropland soil erosion,whereas manure application in combination with seasonal fallow reduces soil erosion.Different crop types as well as cropland location factors determine the spatial pattern of CLDI.Crop rotation modes with major crops of tobacco and maize resulted in a maximal CLDI,and cropland plots with a distance radius of 150 meters away from households received the most intensive physical disturbance.These results are critical to help better protect rural environments in mountainous areas.Based on the results,methods to reduce cropland soil erosion are suggested.展开更多
In this paper,the definition of absolutely balanced and uniformly balanced for graphs are introduced,the difference between balance graphs are pointed out.Using（p,p＋1）-graph as an example,we explained the existence...In this paper,the definition of absolutely balanced and uniformly balanced for graphs are introduced,the difference between balance graphs are pointed out.Using（p,p＋1）-graph as an example,we explained the existence of this difference and obtained some new results.展开更多
Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊ ： E → Z2 defined by f＊（xy） = f（x） ＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i...Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊ ： E → Z2 defined by f＊（xy） = f（x） ＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i） = ｜f＊^-1（i）｜. A labeling f is called friendly if ｜vf（1） - vf（0）｜ ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if（G） = e（1） - el（0）. The set [if（G） ｜ f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI（G）. In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.展开更多
A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and d...A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.展开更多
In this paper, we introduce the concept of the general butterfly graph B[m,n;d] for integers m,n ≥ 3, d ≥ 1, determine its balance index set, and give the necessary and sufficient condition for balanced graph B[m,n;...In this paper, we introduce the concept of the general butterfly graph B[m,n;d] for integers m,n ≥ 3, d ≥ 1, determine its balance index set, and give the necessary and sufficient condition for balanced graph B[m,n;d] to exist.展开更多
Let G be a connected simple graph with vertex set V(G)and edge set E(G).A binary vertex labeling f:V(G)→Z2,is said to be friendly if the number of vertices with different labels differs by at most one.Each vertex fri...Let G be a connected simple graph with vertex set V(G)and edge set E(G).A binary vertex labeling f:V(G)→Z2,is said to be friendly if the number of vertices with different labels differs by at most one.Each vertex friendly labeling/induces an edge labeling f*E(G)→Z2,defined by f*(xy)=f(x)+f(y)for each xy∈E(G).Let er(i)=\{e∈E(G):f*(e)=i}|.The full friendly index set of G,denoted by FFI(G),is the set{ef*(1)-ep(0):f is friendly}.In this paper,we determine the full friendly index set of a family of cycle union graphs which are edge subdivisions of P2×Pn.展开更多
In this paper we will first give the characterization of the p^-low p^-degree,and prove that a p.r.e. degree(?)contains a p^-speedable set A if and only if(?)′>P(?)′.Then we classify the index sets of Low[n]~p an...In this paper we will first give the characterization of the p^-low p^-degree,and prove that a p.r.e. degree(?)contains a p^-speedable set A if and only if(?)′>P(?)′.Then we classify the index sets of Low[n]~p and High[n]~p and prove that Low [n]~p is Σ~P[n+3]-complete and High [n]~p is Σ~P [n+4]-complete.展开更多
基金jointly funded by the National Key Basic Research Program of China (973 program) (Grant NO.2015CB452702)the National Natural Science Foundation of China (Grant NO.41371539)partially supported by the CDM Fund Grant Project in China (Grant NO. 2013030)
文摘Various kinds of human disturbances on cropland are the main reasons for soil erosion and land degradation.Farming practices in mountainous areas vary greatly among cropland plots because of the heterogeneity of biophysical conditions and differences in farmers'management behavior.The main purpose of this paper is to develop a composite index of cropland physical disturbance intensity(CLDI)to reflect the plot-scale discrepancy of potential soil erosion in mountainous areas.The study was based on both plot survey and household interview data,collected from six typical catchments in mountainous areas of southwestern China.Four kinds of physical disturbance practices and two kinds of conservation practices during one crop rotation period were synthesized to develop the CLDI index.The rough set theory was referenced to avoid subjectivity during weight allocation.The results show that conventional tillage,deep fertilization,and manual weeding are the main causes of cropland soil erosion,whereas manure application in combination with seasonal fallow reduces soil erosion.Different crop types as well as cropland location factors determine the spatial pattern of CLDI.Crop rotation modes with major crops of tobacco and maize resulted in a maximal CLDI,and cropland plots with a distance radius of 150 meters away from households received the most intensive physical disturbance.These results are critical to help better protect rural environments in mountainous areas.Based on the results,methods to reduce cropland soil erosion are suggested.
基金Supported by the Natural Science Foundation of Shanxi Province（2008011010） Supported by the Scientific Research and Key Subject Foundation of University of Science and Technology of Suzhou
文摘In this paper,the definition of absolutely balanced and uniformly balanced for graphs are introduced,the difference between balance graphs are pointed out.Using（p,p＋1）-graph as an example,we explained the existence of this difference and obtained some new results.
基金Supported by FRG/07-08/II-08 Hong Kong Baptist University
文摘Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊ ： E → Z2 defined by f＊（xy） = f（x） ＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i） = ｜f＊^-1（i）｜. A labeling f is called friendly if ｜vf（1） - vf（0）｜ ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if（G） = e（1） - el（0）. The set [if（G） ｜ f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI（G）. In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.
文摘A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.
基金the National Natural Science Foundation of China （No. 10671005） the Natural Science Foundation of Hebei Province （No. A2007000230）.
文摘In this paper, we introduce the concept of the general butterfly graph B[m,n;d] for integers m,n ≥ 3, d ≥ 1, determine its balance index set, and give the necessary and sufficient condition for balanced graph B[m,n;d] to exist.
基金This work was supported partly by the National Natural Science Foundation of China(Grant Nos.11801149,11801148)S.Wu was also partially supported by the Doctoral Fund of Henan Polytechnic University(B2018-55).
文摘Let G be a connected simple graph with vertex set V(G)and edge set E(G).A binary vertex labeling f:V(G)→Z2,is said to be friendly if the number of vertices with different labels differs by at most one.Each vertex friendly labeling/induces an edge labeling f*E(G)→Z2,defined by f*(xy)=f(x)+f(y)for each xy∈E(G).Let er(i)=\{e∈E(G):f*(e)=i}|.The full friendly index set of G,denoted by FFI(G),is the set{ef*(1)-ep(0):f is friendly}.In this paper,we determine the full friendly index set of a family of cycle union graphs which are edge subdivisions of P2×Pn.
文摘In this paper we will first give the characterization of the p^-low p^-degree,and prove that a p.r.e. degree(?)contains a p^-speedable set A if and only if(?)′>P(?)′.Then we classify the index sets of Low[n]~p and High[n]~p and prove that Low [n]~p is Σ~P[n+3]-complete and High [n]~p is Σ~P [n+4]-complete.
