ON EDGE MASS ENERGY OF GRAPHS
Sarojini Naik1, Meenal M. Kaliwal2, Vidya S. Umadi3
1Research Scholar, Department of Mathematics, KLS Vishwanathrao Deshpande Institute of Technology, Haliyal-581329, India
2Department of Mathematics, KLS Vishwanathrao Deshpande Institute of Technology, Haliyal 581329, Karnataka State, India
3Department of Mathematics, East Point College of Engineering and Technology, Bengaluru 581329, Karnataka State, India
Let 
be a simple graph of order n and size m, the vertex weight and edge weight is defined as w(vi)=dG(vi) and w(ei) = dG(vi) + dG(vj)-2 for e= vivj. The edge mass adjacency matrix Aw(G) of a graph G is defined in such a way that, for any vi that is adjacent to vj, its (i, j) -entry equals dG(vi) + dG(vj)-2; otherwise, it equals 0 . We look at the Aw(G
‘s EW(G) spectral radius λw1 and energy EW(G). Lower and upper bounds are obtained for λw1 and EW(G) and the respective extremal graphs are characterised. Further we consider a set of 22 benzenoid hydrocarbons and calculate their graph energy and edge mass energy by drawing its molecular graphs. The correlation between physiochemical properties of benzenoid hydrocarbons, molecular descriptors and graph energies are obtained and regression models are studied to check the predictability of physiochemical properties of benzenoid hydrocarbons with E(G) and EW(G).
Keywords: Edge weight energy, spectral radius, benzenoid hydrocarbons, molecular descriptors.