1Deparment of Mathematics, Agni College of Technology, Chennai, India
2Department of Mathematics, Bharathi Women's College, Chennai, India. Email: lavanyaprasad1@gmail.com
3Department of Mathematics, Islamic Azad University Central, Tehran Branch, Tehran, Iran. Email: drsafarisabet@gmail.com
4Department of Mathematics, University of Mazandaran, Babolsar, Iran. Email: a.talebi@umz.ac.ir
5Sama Technical and Vocational Training College, Islamic Azad UniversitySari Branch, Sari, Iran. Email: rashmanlou.1987@gmail.com
*Corresponding author: Email: kishore2982@gmail.com
AMS Mathematics Subject Classification (2010): 05C72, 05C99
Recently, vague graph is a growing research topic as it is the generalization of fuzzy graphs. In this paper, we introduce intense subgraphs and feeble subgraphs based on their densities and discuss mild balanced vague graph and equally balanced vague subgraphs. The operations sum and union of subgraphs of vague graphs are analysed. Likewise, we investigated φ-complement of vague graph structure(VGS) and its isomorphic properties. Finally, an interesting application on vulnerability assessment of gas pipeline systems is given.
Feeble subgraphs, mild balanced vague graphs, φ-complement of vague graph structure
