the geometric-arithmetic index is another topological index was defined as2 deg ( )deg ( )( )deg ( ) deg ( )g guv eg gu vga gu v  , in which degree of vertex u denoted by degg (u). wenow define a new version of ga index as 4( )2 ε ( )ε ( )( )ε ( ) ε ( )g ge uv e g g gu vga g  u v , where εg(u) isthe eccentricity of vertex u. in this paper we compute this new topological index for twogr...

let g and h be two graphs. the corona product g o h is obtained by taking one copy of gand |v(g)| copies of h; and by joining each vertex of the i-th copy of h to the i-th vertex of g,i = 1, 2, …, |v(g)|. in this paper, we compute pi and hyper–wiener indices of the coronaproduct of graphs.

A recently published paper [T. Došlić, this journal 3 (2012) 25-34] considers the Zagreb indices of benzenoid systems, and points out their low discriminativity. We show that analogous results hold for a variety of vertex-degree-based molecular structure descriptors that are being studied in contemporary mathematical chemistry. We also show that these results are straightforwardly obtained by u...

DeepWalk is a typical representation learning method that learns low-dimensional representations for vertices in social networks. Similar to other network representation learning (NRL) models, it encodes the network structure into vertex representations and is learnt in unsupervised form. However, the learnt representations usually lack the ability of discrimination when applied to machine lear...

In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there i...

Because of the associativity of fusion products ⊠, the above hypothesis is equivalent to the condition that for each irreducible module W , there is an irreducible module W̃ such that HomV (W̃ ⊠ W,V ) 6= 0. In the previous paper [6], we have introduced a concept of ”Semi-Rigidity” and then proved that if W is semi-rigid, then W is flat for the fusion products ⊠, that is, 0 → W ⊠ A → W ⊠ B → W ⊠ C...

For a finitely-generated vertex operator algebra V of central charge c ∈ C, a locally convex topological completion HV is constructed. We construct on HV a structure of an algebra over the operad of the c 2 -th power Det c/2 of the determinant line bundle Det over the moduli space of genus-zero Riemann surfaces with ordered analytically parametrized boundary components. In particular, HV is a m...

Traditionally, terrain simplification is time consuming and generates multi-resolution models, from which irregular or semi-regular triangulations are extracted to render a terrain at a suitable level of detail. Recent terrain simplification techniques use GPU-friendly regular grids and apply the filtering and sub-sampling paradigm to generate multiple resolutions. However, such approximations ...