V L−Energy of Graphs
Keywords:
Algebraic graph, V L− connectivity index, V L− connectivity matrix, V L− energy, V L− characteristic polynomialAbstract
Ivan Gutman introduced the concept of Energy of graph in the year 1978. He defined it by taking the adjacency matrix. An adjacency matrix is defined as symmetric matrixes whose entries are one and zero. If two vertices are adjacent then the entry is one. If two vertices are non-adjacent then the entry is zero. Topological indices and Energy of graphs play a vital role in the field of Algebraic Graph Theory and Mathematical Chemistry. The indices are the molecular descriptors, which have a close relationship with the physical and chemical properties of the chemical molecules. Randic matrix is a symmetric matrix which is having entries with Motivated by the Randic matrix, in this paper we introduce the VL-matrix which has entries with This paper deals with the VL energy of graphs. We established the upper and lower bounds. We also generalized the VL-energy for r-regular graphs.
