On some aspects of the generalized Petersen graph

Abstract

Let p ≥ 3 be a positive integer and let k ∈ {1, 2, . . . p − 1}\ p/2 . The generalized Petersen graph GP ((p, k) has its vertex and edge set asIn this paper we probe its spectrum and determine the Estrada index, Laplacian Estrada index, signless Laplacian Estrada index, normalized Laplacian Estrada index, and energy of a graph. While obtaining some interesting results, we also provide relevant background and problems.

Non-isomorphic signatures on some generalised Petersen graph

“…For more on automorphism group of generalised Petersen graph, see [3]. Yegnanarayanan [7] studied various aspects of the generalised Petersen graph.…”

“…The author in [9] determined the non-isomorphic signed Petersen graph, using the fact that the minimum signature on a cubic graph is a matching. Using the same technique, we find the number of non-isomorphic signatures on P (3, 1), P (5, 1) and P (7,1). We also determine the number of non-isomorphic signatures of size two in P (2n + 1, 1) for all n ≥ 1.…”

PEWARNAAN TITIK TOTAL SUPER ANTI-AJAIB LOKAL PADA GRAF PETERSEN DIPERUMUM P(n,k) DENGAN k=1,2

“…Graf Petersen Diperumum 𝑃(𝑛, 𝑘) didefinisikan sebagai graf kubik terhubung yang terdiri dari poligon bintang dalam (𝑛, 𝑘) (graf Circulant 𝐶𝑖 𝑛 (𝑘)) dan poligon beraturan luar n (graf Cycle 𝐶 𝑛 ) dengan titik-titik yang bersesuaian pada poligon dalam dan luar yang terhubung dengan sisi. Misalkan 𝑛 ≥ 3 adalah sebuah bilangan positif dan 𝑘 ∈ {1,2, … , 𝑛 − 1}\⌊𝑛/2⌋ [6]. Graf Petersen Diperumum 𝑃(𝑛, 𝑘) mempunyai himpunan titik 𝑉(𝑃(𝑛, 𝑘)…”

Edge Irregular Reflexive Labeling for Disjoint Union of Generalized Petersen Graph

“…Gera et al [36] completely describe the spectrum of the Generalized Petersen graph P(n, m). Yegnanarayanan [37] computed the spectrum, the Estrada index, Laplacian Estrada index, signless Laplacian Estrada index, normalized Laplacian Estrada index, and energy of Generalized Petersen graph P(n, m).…”