This paper introduces an approach to locating dependence structures in a program by searching the space of the powerset of the set of all possible program slices. The paper formulates this problem as a search based software engineering problem. To evaluate the approach, the paper introduces an instance of a search based slicing problem concerned with locating sets of slices that decompose a pro...

A dominating set S of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LDcodes and the cardinality of an LD-code is the location-domination number, λ(G). An LD-set S of a graph G is global if it is an LD-set for both G and its complem...

A dominating set S of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LDcodes and the cardinality of an LD-code is the location-domination number, λ(G). An LD-set S of a graph G is global if it is an LD-set for both G and its complem...

Consider a matrix valued function A(x) ∈ R, m ≥ n, smoothly depending on parameters x ∈ Ω ⊂ R, where Ω is simply connected and bounded. We consider a technique to locate parameter values where some of the q dominant (q ≤ n) singular values of A coalesce, in the specific case when A is large and m > n ≫ q. Notation. An m × n real matrix is indicated with A ∈ Rm×n. We always consider the 2-norm f...

‎let $f$ be a proper $k$-coloring of a connected graph $g$ and‎ ‎$pi=(v_1,v_2,ldots,v_k)$ be an ordered partition of $v(g)$ into‎ ‎the resulting color classes‎. ‎for a vertex $v$ of $g$‎, ‎the color‎ ‎code of $v$ with respect to $pi$ is defined to be the ordered‎ ‎$k$-tuple $c_{{}_pi}(v)=(d(v,v_1),d(v,v_2),ldots,d(v,v_k))$‎, ‎where $d(v,v_i)=min{d(v,x):~xin v_i}‎, ‎1leq ileq k$‎. ‎if‎ ‎distinct...

Let G be a connected graph with vertex set V (G) and edge E(G). The open hop neighborhood of v ∈ is the NG(v, 2) = {w : dG(v, w) 2}, where denotes distance between w. A non-empty S ⊆ locating if NG(u, ∩ ̸= for every pair distinct vertices u, \ S. smallest cardinality G, denoted by lhn(G) called number G. This study focuses mainly on concept in graphs. Characterizations sets join corona two graph...

A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number λ(G). An LD-set S of a graph G is global if it is an LD-set of both G and its complem...

Let c be a proper k-coloring of a connected graph G. Let Π = {S1, S2, . . . , Sk} be the induced partition of V (G) by c, where Si is the partition class having all vertices with color i. The color code cΠ(v) of vertex v is the ordered k-tuple (d(v, S1), d(v, S2), . . . , d(v, Sk)), where d(v, Si) = min{d(v, x)|x ∈ Si}, for 1 ≤ i ≤ k. If all vertices of G have distinct color codes, then c is ca...

A set S ⊆ V (G) of an undirected graph G is a locating-dominating if for each v ∈ \ S, there exists w such tha vw E(G) and NG(x) ∩ ̸= NG(y) any two distinct vertices x y in S. stable it {v} The minimum cardinality G, denoted by γSLD(G), called the locating-domination number G. In this paper, we investigate concept corresponding parameter edge corona lexicographic product graphs.