On the F-index and F-coindex of the line graphs of the subdivision graphs

Amin, Ruhul; Nayeem, Sk. Md. Abu

doi:10.26637/mjm0602/0010

Cited by 3 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“… 2017 Akhtar et al [ 2 ] They have find maximal unicyclic graph with respect to the F-index for crisp graph. 2018 Amin et al [ 7 ] They have studied F-index and F-coindex of the line graphs of the subdivision graphs. 2019 Binu et al [ 8 ] They have introduced the connectivity index for fuzzy graphs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Further development of F-index for fuzzy graph and its application in Indian railway crime

Islam

Pal

2022

J. Appl. Math. Comput.

View full text Add to dashboard Cite

From the mid-nineteenth century, the railway network has been the most important mode of conveying people and goods in India. 22.15 million passengers used this network and 3.32 million metric tons of goods were also shipped daily from 2019 to 2020. The national rail network comprised 126,366 km of track over a route of 67,368 km and 7,325 stations. It is the fourth-largest national railway network globally after the United States, Russia and China. But with the passage, they pose a threat to the general public while travelling, being the instances of crimes rising fourfold in rails. The ongoing railway crime has become a cause of concern for the common passenger now. In this article, F-index for fuzzy graphs is used to analyze the railway crimes in India and compared with three other topological indices. F-index for fuzzy graphs and the first Zagreb index for fuzzy graphs provide similar results whereas F-index for fuzzy graphs provides better realistic results than F-index for crisp graphs and first Zagreb index for crisp graphs to detect the crime in Indian railway. Also, this index is studied for several operations such as Cartesian product, composition, union and join of two fuzzy graphs. Some interesting relations of F-index are established during fuzzy graph transformations. Using those transformation, it is shown that n -vertex star has maximum F-index among the n -vertex trees. Also, maximal n -vertex unicyclic fuzzy graph having r cycle is determined with respect to F-index.

show abstract

Section: Introductionmentioning

confidence: 99%

“…In 2015, Fortula and Gutman defined another degree-based topological index called forgotten topological index (F-index) [ 14 ]. Amin and Nayeem studied the F-index and F-coindex of subdivision graph and line graph in [ 7 ]. In 2017, Abdo et al [ 1 ] studied the extremal trees (crisp) with respect to F-index.…”

Section: Introductionmentioning

confidence: 99%