“…Later, (Rosenfeld, 1975) defined the basic properties of fuzzy relations which are generalized with fuzzy set as a base set and fuzzy analogues of graphic theoretical concepts like bridges and trees were established with their properties and further fuzzy graph concepts were developed and applied in the real life situations in (Mohamed et al, 2020;Mordeson & Chang-Shyh, 1994;Naz et al, 2017Quek, et al, 2018 ;Smarandache, 2013 ;Tan et al, 2021 ;Das et al, 2021 ;Majumder et al, 2021;Saha et al, 2022). Recent developments of the fuzzy extensions are developed as in (Kumar et al, 2019 ;Radha et al,2021 ;Vellapandi & Gunasekaran, 2020 ;Das & Edalatpanah, 2020 ;Polymenis, 2021;Mao et al, 2020 ;Voskoglou & Broumi, 2022 ;Zhang et al, 2022 ;Al-Hamido, 2022). To the best of authors knowledge, a very less work is being done on the interval-valued pentapartitioned neutrosophic set (IVPPNS), so the present study define the operations on the IVPPNS and later on extend it to graphs environment.…”