The Edge-To-Vertex Triangle Free Detor Distance in Graphs

Authors

  • S Lourdu Elqueen Reg No: 19212212092009, Ph. D Research Scholar (Full Time) of Mathematics. Mary’s College (Autonomous) Thoothukudi affiliated underManonmaniam Sundaranar University,Abishekapatti,Tirunelveli, Tamil Nadu
  • G Priscilla Pacifica Department of Mathematics, St. Mary’s College (Autonomous), Thoothukudi,

DOI:

https://doi.org/10.23755/rm.v44i0.894

Keywords:

connected graph, edge -to-vertex distance and edge-to-vertex detour distance

Abstract

For every connected graph G, the triangle free detour distance D∆f(u, v) is the length of a longest u- v triangle free path in G, where u, v are the vertices of G.  A u-v triangle free path of length D∆f(u, v) is called the u-v triangle free detour. In this article, the edge-to-vertex triangle free detour distance is introduced. It is found that the edge -to-vertex triangle free detour distance differs from the edge -to-vertex distance and edge-to-vertex detour distance. The edge-to-vertex triangle free detour distance is found for some standard graphs. Their bounds are determined and their sharpness is checked. Certain general properties satisfied by them are studied.

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Published

2022-12-11

Issue

Vol. 44 (2022): Special Issue: Recent Trends in Mathematics and its Applications

Section

Volume 45-2023

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