New Concepts on Mild Balanced Vague Graphs with Application Kumar P.K. Kishore1,*, Lavanya S.2, Safarisabet Sh. A.3, Talebi A.A.4, Rashmanlou Hossein5 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 Online published on 7 February, 2019. Abstract 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. Top Keywords Feeble subgraphs, mild balanced vague graphs, φ-complement of vague graph structure. Top |