Abstract This paper presents a method to estimate the covariances of inputs in factor-graph formulation for localization under non-line-of-sight conditions. A general solution based on covariance estimation and M-estimators linear regression problems, is presented that shown give unbiased estimators multiple variances are robust against outliers. An iteratively re-weighted least squares algorit...

We introduce a generalization of competition graphs, called weighted competition graphs. The weighted competition graph of a digraph D = (V,A), denoted by Cw(D), is an edge-weighted graph (G,w) such that G = (V,E) is the competition graph of D, and the weight w(e) of an edge e = xy ∈ E is the number of the common preys of x and y in D. We investigate properties of weighted competition graphs.

An interval coloring of a weighted graph with non-negative weights, maps each vertex onto an open interval on the real line with width equal to the weight of the vertex, such that adjacent vertices are mapped to disjoint intervals. The total width of an interval coloring is defined as the width of the union of the intervals. The interval chromatic number of a weighted graph is the least total w...

This paper proposes an algorithm for buUdmg weighted directed graph,defmes the weighted directed relationship matrix of the graph,an d describes algorithm implementation using this matrix.Based on this algorithm ,an effective way for building an d drawing weighted directed graphs is presented,forming a foundation for visual implementation of the algorithm in the graph theory.

Let T be an edge-labeled graph, where the labels are from a finite alphabet Σ. For a subtree U of T , the Parikh vector of U is a vector of length |Σ| which specifies the multiplicity of each label in U . We ask when T can be reconstructed from the multiset of Parikh vectors of all of its subtrees, or all of its paths, or all of its maximal paths. We consider the analogous problems for weighted...

‎let $g=(v(g),e(g))$ be a simple connected graph with vertex set $v(g)$ and edge‎ ‎set $e(g)$‎. ‎the (first) edge-hyper wiener index of the graph $g$ is defined as‎: ‎$$ww_{e}(g)=sum_{{f,g}subseteq e(g)}(d_{e}(f,g|g)+d_{e}^{2}(f,g|g))=frac{1}{2}sum_{fin e(g)}(d_{e}(f|g)+d^{2}_{e}(f|g)),$$‎ ‎where $d_{e}(f,g|g)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $e(g)$ and $d_{e}(f|g)=s...