Hoàng defined the P4-sparse graphs as the graphs where every set of five vertices induces at most one P4. These graphs attracted considerable attention in connection with the P4-structure of graphs and the fact that P4-sparse graphs have bounded clique-width. Fouquet and Giakoumakis generalized this class to the nicely structured semi-P4-sparse graphs being the (P5, co-P5, co-chair)-free graphs...

The graph construction procedure essentially determines the potentials of those graph-oriented learning algorithms for image analysis. In this paper, we propose a process to build the so-called directed l1-graph, in which the vertices involve all the samples and the ingoing edge weights to each vertex describe its l1-norm driven reconstruction from the remaining samples and the noise. Then, a s...

Fox, Gromov, Lafforgue, Naor, and Pach proved a regularity lemma for semi-algebraic kuniform hypergraphs of bounded complexity, showing that for each ǫ > 0 the vertex set can be equitably partitioned into a bounded number of parts (in terms of ǫ and the complexity) so that all but an ǫ-fraction of the k-tuples of parts are homogeneous. We prove that the number of parts can be taken to be polyno...

We derive L 1 bounds for norms of projections onto bivariate polynomial spline spaces on regular triangulations with stable local bases. We then apply this result to derive error bounds for best L 2-and`2-approximation by splines on quasi-uniform triangulations. x1. Introduction Let X L 1 (() be a linear space deened a set with polygonal boundary. Suppose hh; i is a semi-deenite inner-product o...

the vertex-edge wiener index of a simple connected graph g is defined as the sum of distances between vertices and edges of g. two possible distances d_1(u,e|g) and d_2(u,e|g) between a vertex u and an edge e of g were considered in the literature and according to them, the corresponding vertex-edge wiener indices w_{ve_1}(g) and w_{ve_2}(g) were introduced. in this paper, we present exact form...

let g be a simple graph with vertex set v(g) {v1,v2 ,...vn} . for every vertex i v , ( ) i  vrepresents the degree of vertex i v . the h-th order of randić index, h r is defined as the sumof terms1 2 11( ), ( )... ( ) i i ih  v  v  vover all paths of length h contained (as sub graphs) in g . inthis paper , some bounds for higher randić index and a method for computing the higherrandic ind...

‎let $g$ be a graph with vertex set $v(g)$ and edge set $x(g)$ and consider the set $a={0,1}$‎. ‎a mapping $l:v(g)longrightarrow a$ is called binary vertex labeling of $g$ and $l(v)$ is called the label of the vertex $v$ under $l$‎. ‎in this paper we introduce a new kind of graph energy for the binary labeled graph‎, ‎the labeled graph energy $e_{l}(g)$‎. ‎it depends on the underlying graph $g$...