[PDF][PDF] On some aspects of the generalized Petersen graph.
V Yegnanarayanan - Electron. J. Graph Theory Appl., 2017 - academia.edu
Electron. J. Graph Theory Appl., 2017•academia.edu
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 as V (GP (p, k))={ui: i∈ Zp}∪{u′ i: i∈ Zp} and E
(GP (p, k))={uiui+ 1: i∈ Zp}∪{u′ iu′ i+ k∈ Zp}∪{uiu′ i: i∈ Zp}. In 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.
graph GP ((p, k) has its vertex and edge set as V (GP (p, k))={ui: i∈ Zp}∪{u′ i: i∈ Zp} and E
(GP (p, k))={uiui+ 1: i∈ Zp}∪{u′ iu′ i+ k∈ Zp}∪{uiu′ i: i∈ Zp}. In 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.
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 as V (GP (p, k))={ui: i∈ Zp}∪{u′ i: i∈ Zp} and E (GP (p, k))={uiui+ 1: i∈ Zp}∪{u′ iu′ i+ k∈ Zp}∪{uiu′ i: i∈ Zp}. In 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.
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