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...

UNLABELLED Most cellular tasks are performed not by individual proteins, but by groups of functionally associated proteins, often referred to as modules. In a protein association network modules appear as groups of densely interconnected nodes, also called communities or clusters. These modules often overlap with each other and form a network of their own, in which nodes (links) represent the m...

In this paper we compute for paths and cycles certain graph domination invariants like locating domination number, differentiating domination number, global alliance number etc., We also do some comparison analysis of certain parameters defined by combining the domination measures and the second smallest eigen value of the Laplacian matrix of all connected graphs of order 4.While discussing app...

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

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...

We study the approximability and inapproximability of finding identifying codes and locating-dominating codes of the minimum size. In general graphs, we show that it is possible to approximate both problems within a logarithmic factor, but sublogarithmic approximation ratios are intractable. In bounded-degree graphs, there is a trivial constant-factor approximation algorithm, but arbitrarily lo...

An identifying code is a subset of vertices of a graph with the property that each vertex is uniquely determined (identified) by its nonempty neighbourhood within the identifying code. When only vertices out of the code are asked to be identified, we get the related concept of a locating-dominating set. These notions are closely related to a number of similar and well-studied concepts such as t...