Abstract In this paper, the exact formulae for the Harary indices of join, disjunction, symmetric difference, strong product of graphs are obtained. Also, the Schultz and modified Schultz indices of join and strong product of graphs are computed. We apply some of our results to compute the Harary, Schultz and modified Schultz indices of fan graph, wheel graph, open fence and closed fence graphs.

We study a new search problem on the plane involving a robot and an immobile treasure, initially placed at distance 1 from each other. The length β of an arc (a fence) within the perimeter of the corresponding circle, as well as the promise that the treasure is outside the fence, is given as part of the input. The goal is to device movement trajectories so that the robot locates the treasure in...

Free-roaming cats are exposed to a variety of risks, including involvement in road traffic accidents. One way of mitigating these risks is to contain cats, for example using an electronic boundary fence system that delivers an electric 'correction' via a collar if a cat ignores a warning cue and attempts to cross the boundary. However, concerns have been expressed over the welfare impact of suc...

The increasing availability of GPS-enabled mobile devices can utilize position to provide a safer tracked environment allowing vulnerable people to continue with their daily activities, as much as possible. This paper investigates the technology options for alert escalation. The aim is to provide a safety net, without triggering unnecessary alarms. The escalation procedure involves initial spee...