<abstract><p>Let $ G be a graph with vertex set V(G) $. A function f:V(G)\rightarrow \{0, 1, 2\} is Roman dominating on if every v\in for which f(v) = 0 adjacent to at least one u\in such that f(u) 2 The domination number of the minimum weight \omega(f) \sum_{x\in V(G)}f(x) among all functions f In this article we study direct product graphs and rooted graphs. Specifically, give sev...

Let G be a graph with no isolated vertex and let N(v) the open neighbourhood of v∈V(G). f:V(G)→{0,1,2} function Vi={v∈V(G):f(v)=i} for every i∈{0,1,2}. We say that f is strongly total Roman dominating on if subgraph induced by V1∪V2 has N(v)∩V2≠∅ v∈V(G)\V2. The domination number G, denoted γtRs(G), defined as minimum weight ω(f)=∑x∈V(G)f(x) among all functions G. This paper devoted to study it ...

The uniform capacitated vertex k -center problem is an \(\mathcal {NP} \) -hard combinatorial optimization that models real situations where centers can only attend a maximum number of customers, and the travel time or distance from customers to their assigned center has be minimized. This paper introduces polynomial-time constructive heuristic algorithm exploits relationship between this minim...

Purpose: To assess the reliability of neurocognitive and functional performance tests in athletes with and without functional ankle instability (FAI). Methods: In this methodological study, 20 athletes with unilateral functional ankle instability (mean age [SD]: 23.40[2.58] y; mean height[SD]: 1.77[0.11] m; mean weight[SD]: 67.00[13.18] kg) and 20 uninjured athletes (mean age[SD]: 23.05[2.72] ...

A unit disk graph G on a given set P of points in the plane is geometric where an edge exists between two p,q∈P if and only |pq|≤1. spanning subgraph G′ k-hop spanner for every pq∈G, there path p,q with at most k edges. We obtain following results graphs plane. Every n-vertex has 5-hop 5.5n analyze family spanners constructed by Biniaz (2020) improve upper bound number edges from 9n to 5.5n. Us...

Finding the minimum connected dominating set (MCDS) is a key problem in wireless sensor networks, which is crucial for efficient routing and broadcasting. However, the MCDS problem is NP-hard. In this paper, a new approximation algorithm with approximation ratio H( )+ 3 in time O n2 is proposed to approach the MCDS problem. The key idea is to divide the sensors in CDS into core sensors and supp...

Wireless communication has seen a tremendous growth in the last decades. Continuing on this trend, wireless multi-hop networks are nowadays used or planned for use in a multitude of contexts, spanning from Internet access at home to emergency situations. The Transmission Control Protocol (TCP) provides reliable and ordered delivery of a data and is used by major Internet applications such as we...

Given an undirected graph G = (V,E) and a weight function w : E → R, the Minimum Dominating Tree problem asks to find a minimum weight sub-tree of G, T = (U,F ), such that every v ∈ V \U is adjacent to at least one vertex in U . The special case when the weight function is uniform is known as the Minimum Connected Dominating Set problem. Given an undirected graph G = (V,E) with some subsets of ...