The inflation $G_{I}$ of a graph $G$ with $n(G)$ vertices and $m(G)$ edges is obtained from $G$ by replacing every vertex of degree $d$ of $G$ by a clique, which is isomorph to the complete graph $K_{d}$, and each edge $(x_{i},x_{j})$ of $G$ is replaced by an edge $(u,v)$ in such a way that $uin X_{i}$, $vin X_{j}$, and two different edges of $G$ are replaced by non-adjacent edges of $G_{I}$. T...

Image may contain shadow, which can lead to serious problem for full exploitation of image. This paper proposes A Novel Processing Chain to solve this problem. The main aim of this chain process is not only detect shadow region form image but also remove shadow region and reconstruct shadow less image. In this chain process, initially we classified shadow vs. nonshadow region by using binary cl...

Let $G$ be a graph and let $m_{ij}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The {em $M$-polynomial} of $G$ is introduced with $displaystyle{M(G;x,y) = sum_{ile j} m_{ij}(G)x^iy^j}$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

Given a configuration of indistinguishable pebbles on the vertices of a connected graph G on n vertices, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one pebble on an adjacent vertex. The m-pebbling number of a graph G, πm(G), is the smallest integer k such that for each vertex v and each configuration of k pebbles on G there is a sequence of p...

Graph classification, which aims to identify the category labels of graphs, plays a significant role in drug toxicity detection, protein analysis etc. However, limitation scale benchmark datasets makes it easy for graph classification models fall into over-fitting and undergeneralization. To improve this, we introduce data augmentation on graphs (i.e. augmentation) present four methods:random m...