a. To check that the graph is represented correctly, Bob asks Alice to remove all the paper cups covering the endpoints of every edge. This reveals an isomorphism to the original graph, which Bob cannot check efficiently; thus, Bob also removes the paper cups corresponding to the green numbers, revealing the original labelling of the vertices. This reveals nothing about the vertex cover, but al...

In this paper we show that the one-loop graviton self-energy contribution is ultraviolet finite, without introducing counterterms, and cutoff-free in the framework of causal perturbation theory. In addition, it satisfies the gravitational Slavnov–Ward identities for the two-point connected Green function. The condition of perturbative gauge invariance to second order for loop graphs is proved. ...

We generalize a construction of the Néron model for a family of intermediate Jacobians due to Green, Griffiths and Kerr by using the theory of mixed Hodge modules. It is a topological group defined over any partial compactification of the base space, and it ‘graphs’ admissible normal functions. Moreover, there is a stratification of the partial compactification such that the restriction over ea...

We explain the concept of worldline Green functions on classes of multiloop graphs. The QED β – function and the 2-loop Euler-Heisenberg Lagrangian are discussed for illustration. HD-THEP-96/44 HUB-EP-96/29 ∗Talk presented by M.G.Schmidt at the Dubna Joint Meeting: International Seminar on Path Integrals: Theory and Applications, and 5th International Conference on Path Integrals from meV to Me...

Thoughts on Matching Data The primary lights are not unique, and the same facts can be presented in alternate sets of graphs, an awkward situation. However, ! Wright and Guild both used red, green, and blue primaries. They are not totally arbitrary. ! The mixing of 3 primaries directly models such technologies as television. The experiment is not a strange one. ! A practical questio...

the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...

we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $...

In the present work, a modified model of heat conduction including higher order of time derivative is derived by extending Green and Naghdi theory without energy dissipation. We introduce two phase lag times to include the thermal displacement gradient and the heat flux in the heat conduction and depict microscopic responses more precisely. The constructed model is applied to s...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...