Open AccessEccentric connectivity index of identity graph of cyclic group and finite commutative ring with unity
Author(s) -
Abdussakir Abdussakir,
Lila Puspitasari,
Wahyu Henky Irawan,
Evawati Alisah
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1375/1/012067
Subject(s) - mathematics , combinatorics , vertex (graph theory) , graph , commutative ring , topological index , discrete mathematics , connectivity , cubic graph , voltage graph , pure mathematics , line graph , commutative property
Research on graph associated with a finite algebraic structure has attracted many attentions. On the other hand, eccentric connectivity index is an interesting topic and many studies have been reported. For simple connected graph G , let e ( v ) denoted the eccentricity of vertex v and deg ( v ) denoted the degree of vertex v in G . Eccentric connectivity index of G is defined as the sum of all e ( v ) deg ( v ), for any v in G . We focus the study on determining eccentricity connectivity index of identity graph of cyclic group and finite commutative ring with unity. We present the exact formula for eccentricity connectivity index of identity graph of these two algebraic structures.