This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a s...This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic labeling the vertices receive the smallest labels and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s appearing in the graph. The paper examines the existence of such labelings for plane graphs containing a special Hamilton path.展开更多
A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}...A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}. In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees （mT）, all of them of the same order, grows at least exponentially with m.展开更多
Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,...Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,... ,p ＋ q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f（x） assigned to the vertex x together with all values f（xy） assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1,..., r ＋ 1.展开更多
Glioblastoma is a highly aggressive brain tumor,very invasive and thus difficult to eradicate with standard oncology therapies.Bioelectric treatments based on pulsed electric fields have proven to be a successful meth...Glioblastoma is a highly aggressive brain tumor,very invasive and thus difficult to eradicate with standard oncology therapies.Bioelectric treatments based on pulsed electric fields have proven to be a successful method to treat cancerous tissues.However,they rely on stiff electrodes,which cause acute and chronic injuries,especially in soft tissues like the brain.Here we demonstrate the feasibility of delivering pulsed electric fields with flexible electronics using an in ovo vascularized tumor model.We show with fluorescence widefield and multiphoton microscopy that pulsed electric fields induce vasoconstriction of blood vessels and evoke calcium signals in vascularized glioblastoma spheroids stably expressing a genetically encoded fluorescence reporter.Simulations of the electric field delivery are compared with the measured influence of electric field effects on cell membrane integrity in exposed tumor cells.Our results confirm the feasibility of flexible electronics as a means of delivering intense pulsed electric fields to tumors in an intravital 3D vascularized model of human glioblastoma.展开更多
文摘This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic labeling the vertices receive the smallest labels and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s appearing in the graph. The paper examines the existence of such labelings for plane graphs containing a special Hamilton path.
基金Supported by the Slovak VEGA (Grant No.1/4005/07)Spanish Research Council (Grant No.BFM2002-00412)
文摘A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}. In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees （mT）, all of them of the same order, grows at least exponentially with m.
基金Supported by Slovak VEGA Grant 1/0130/12Higher Education Commission Pakistan (Grant No.HEC(FD)/2007/555)the Ministry of Education of the Czech Republic (Grant No. MSM6198910027)
文摘Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,... ,p ＋ q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f（x） assigned to the vertex x together with all values f（xy） assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1,..., r ＋ 1.
基金supported by the French National Research Agency(ANR-18-CE19-0029).
文摘Glioblastoma is a highly aggressive brain tumor,very invasive and thus difficult to eradicate with standard oncology therapies.Bioelectric treatments based on pulsed electric fields have proven to be a successful method to treat cancerous tissues.However,they rely on stiff electrodes,which cause acute and chronic injuries,especially in soft tissues like the brain.Here we demonstrate the feasibility of delivering pulsed electric fields with flexible electronics using an in ovo vascularized tumor model.We show with fluorescence widefield and multiphoton microscopy that pulsed electric fields induce vasoconstriction of blood vessels and evoke calcium signals in vascularized glioblastoma spheroids stably expressing a genetically encoded fluorescence reporter.Simulations of the electric field delivery are compared with the measured influence of electric field effects on cell membrane integrity in exposed tumor cells.Our results confirm the feasibility of flexible electronics as a means of delivering intense pulsed electric fields to tumors in an intravital 3D vascularized model of human glioblastoma.
文摘The paper describes magic labelings of type (1,1,1) for two classes of graphs, which are obtained by a combination of vertex, edge and face labelings.
