A_α-energy of graphs formed by some unary operations

2024/04/05 by V K Najiya, K, Najiya V, A V Chithra +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2404.03905

openalex publication_date 2024/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a graph on p vertices with adjacency matrix A(G) and degree matrix D(G). For each α∈ [0, 1], the A_α-matrix is defined as A_α(G) = αD(G) + (1 - α)A(G). In this paper, we compute the A_α-characteristic polynomial, A_α-spectra and A_α-energy of some non-regular graphs obtained from unary operations on graphs like middle graph, central graph, m-splitting, and closed splitting graph. Also, we determine the A_α-energy of regular graphs like m-shadow, closed shadow, extended bipartite double graph, iterated line graph and m-duplicate graph. Furthermore, we identified some graphs that are A_α-equieneregetic and A_α-borderenergetic.

Related

• On the eigenvalues and energy of the A_α-matrix of graphs
• On the characteristic polynomial of the A_α-matrix for some operations of graphs
• On the Characteristic polynomial of ABS Matrix and ABS-Energy of Some Graphs
• A lower bound of the energy of non-singular graphs in terms of average degree
• The A_α-spectra of graph operations based on generalized (edge) corona