On metric dimension of symmetrical planer pyramid related graphs

Abstract

Abstract Robotics and networking have transformed the world in numerous ways. Nowadays, computer networks play a vital role not only in business, education, and medical treatments, but also in entertainment. Graph theory has wide-ranging applications in robotics, tricky games, computer networking, map formations, image processing, Loran or Sonar models, pattern recognition, artificial intelligence, medical networks (such as oxygen or other treatment wiring), navigation problems, electrical networks, and more. Metric dimension has left its mark on artificial intelligence, map navigation, image recognition, pattern formation, facility location problems, and resource management (cost, time, labor, and resources). Robots are used in almost every field of life, including saving lives in the medical field, and metric dimension plays a crucial role in ensuring their accuracy. In this recent work, we enhance the concept of reflection of graphs and introduce new graphs, which we have called horizontal reflection graphs. We also compute the metric dimension of $$h-Vrl(mid(Tower_{p}))$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>-</mml:mo> <mml:mi>V</mml:mi> <mml:mi>r</mml:mi> <mml:mi>l</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mi>i</mml:mi> <mml:mi>d</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mi>o</mml:mi> <mml:mi>w</mml:mi> <mml:mi>e</mml:mi> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and h-Vrl(Middle tower Path Graph) and found it to be constant.