On Extended Adjacency Index with Respect to Acyclic, Unicyclic and Bicyclic Graphs

• Main Authors: Bin Yang, Vinayak V. Manjalapur, Sharanu P. Sajjan, Madhura M. Mathai, Jia-Bao Liu
• Format: Article
• Language: English
• Published: MDPI AG 2019-07-01
• Series: Mathematics
• Subjects: degree of vertex; extended adjacency index
• Online Access: https://www.mdpi.com/2227-7390/7/7/652

For a (molecular) graph <i>G</i>, the extended adjacency index <inline-formula> <math display="inline"> <semantics> <mrow> <mi>E</mi> <mi>A</mi> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> is defined as Equation (1). In this paper we introduce some graph transformations which increase or decrease the extended adjacency (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>E</mi> <mi>A</mi> </mrow> </semantics> </math> </inline-formula>) index. Also, we obtain the extremal acyclic, unicyclic and bicyclic graphs with minimum and maximum of the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>E</mi> <mi>A</mi> </mrow> </semantics> </math> </inline-formula> index by a unified method, respectively.