New Concepts on Mild Balanced Vague Graphs with Application

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.