Vertex Energy of Small Integral Graphs
Vertex Energy of Small Integral Graphs
Abstract
The energy of a graph, introduced in 1970's, is a well studied spectrum based graph invariant that has a notable number of applications in different fields of science. Recently, Arizmendi et al. have reworked on this idea by introducing the concept of vertex energy of a graph which reflects upon the way the total energy is distributed among the individual vertices. Further, they have explained a method of computing the energy of a vertex $v$ by means of solving a system of linear equations involving the number of $v-v$ walks of different lengths from $v$. In the present study, we compute the vertex energies for all non-trivial connected integral graphs of order up to seven using this method.
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