We introduce a novel algorithm for the efficient detection and tracking of features in spatiotemporal atmospheric data, as well as for the precise localization of the occurring genesis, lysis, merging and splitting events. The algorithm works on data given on a four-dimensional structured grid. Feature selection and clustering are based on adjustable local and global criteria, feature tracking ...

Let G = (V, E) be a graph with V = S1 S2 ...,St T where each Si is a set of vertices having at least two vertices and having the same degree and T = V Si. The degree splitting graph of G is denoted by DS(G) is obtained from G by adding vertices w1, w2, ..., wt and joining wi to each vertex of Si (1  i  t). Let the vertices and the edges of a graph G are called the elements of G. In this...

Given a tree and a set P of non-trivial simple paths on it, Vpt(P) is the VPT graph (i.e. the vertex intersection graph) of the paths P of the tree T , and Ept(P) is the EPT graph (i.e. the edge intersection graph) of P. These graphs have been extensively studied in the literature. Given two (edge) intersecting paths in a graph, their split vertices is the set of vertices having degree at least...

A  $ mu $-way  $ G $-trade ($ mu geq 2) $  consists of $ mu $ disjoint decompositions of some simple (underlying) graph $ H $ into copies of a graph $ G. $  The   number of copies of the  graph $ G $ in  each of the decompositions is the volume of the $ G $-trade and   denoted by $ s. $ In this paper, we determine all values  $ s $ for which there exists a $  mu $-way   $ K_{1,m} $-trade of  vo...

Let $G=(V,E)$, $V={v_1,v_2,ldots,v_n}$, be a simple graph with$n$ vertices, $m$ edges and a sequence of vertex degrees$Delta=d_1ge d_2ge cdots ge d_n=delta$, $d_i=d(v_i)$. Ifvertices $v_i$ and $v_j$ are adjacent in $G$, it is denoted as $isim j$, otherwise, we write $insim j$. The first Zagreb index isvertex-degree-based graph invariant defined as$M_1(G)=sum_{i=1}^nd_i^2$, whereas the first Zag...

In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed...

We consider an unweighted undirected graph with n vertices, m edges, and edge-connectivity 2k. The weak edge orientation problem requires that the edges of this graph be oriented so the resulting directed graph is at least k edge-connected. Nash-Williams proved the existence of such orientations and subsequently Frank [6], Gabow [7], and Nagamochi-Ibaraki [12] gave algorithmic constructions. Al...

let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...

The splitting number of a graph G consists in the smallest positive integer k 0, such that a planar graph can be obtained from G by k splitting operations, such operation replaces v by two nonadjacent vertices v1 and v2, and attaches the neighbors of v either to v1 or to v2. One of the most useful graphs in computer science is the n{cube. Dean and Richter devoted an article to proving that the ...