Abstract
Let Z be the simple graph; then, we can obtain the energy E(Z) of a graph Z by taking the absolute sum of the eigenvalues of the adjacency matrix of Z. In this research, we have computed different energy invariants of the noncompleted extended P‐Sum (NEPS) of graph Zi. In particular, we investigate the Randic, Seidel, and Laplacian energies of the NEPS of path graph with any base ℬ. Here, n denotes the number of vertices and i denotes the number of copies of path graph Pn. Some of the results depend on the number of zeroes in base elements, for which we use the notation j.
Highlights
Introduction enoncompleted extended P-Sum (NEPS) of the graphs is a graph Z whose vertex set is equal to the simple Cartesian product of the vertices’ sets of the graphs [1]
In [7], Haemers defined the Seidel energy; let the Seidel matrix of a graph G be represented as SE(G), and θi are the eigenvalues of this matrix; the energy of graph is the summation of |θi|, where θ − i is of the Seidel matrix
If the eigenvalues of the Laplacian matrix is denoted by μi, the Laplacian energy of the graph Z is expressed as LE(Z) n μi − d(Z), (8)
Summary
Introduction eNEPS of the graphs is a graph Z whose vertex set is equal to the simple Cartesian product of the vertices’ sets of the graphs [1]. En, how this result is used in calculating Randic, Seidel, and Laplacian energy of this graph? E energy of the graph Z is defined as the absolute sum of the eigenvalues of the adjacency matrix of Z.
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