Eccentricity energy of bistar graph and some of its related graphs

Khunti, Shanti S.; Gadhiya, Jekil A.; Chaurasiya, Mehul A.; Rupani, Mehul P.

doi:10.26637/mjm0804/0021

Cited by 1 publication

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…"A unit x is unipotent if there is nilpotent z such that x = 1 + z and ring whose units are all unipotents is called UU ring (6) ". "Bistar B k,k is graph obtained from K 2 by joining centers of 2K 1,n by an edge (7) ".…”

Section: Introductionmentioning

confidence: 99%

Connectedness in Projection Graphs of Commutative Rings

Arockiamary,

Meera,

Santhi

2023

IJST

View full text Add to dashboard Cite

Background/Objectives: Connectedness plays an essential role in applications of graph theory. Connected graphs are used to represent social networks, transportation networks, and communication networks. In this study, various classes of commutative rings are explored to identify connected projection graphs. Methods: An investigation is carried out to exclude classes of rings whose projection graphs possess isolated vertices and connectedness is shown by establishing spanning subgraphs. Findings : Unipotent units and zero-divisors are found non-isolated, in which zero-divisors include idempotents and nilpotents. The element 2 is isolated if it is invertible. Necessary condition for the rings to have connected projection graphs is derived. Projection graphs of finite Boolean rings are connected and Hamiltonian. The local rings of integers modulo n with even characteristics are connected and contain spanning bistars. A criterion for certain class of nonlocal rings to have connected projection graphs is described. Novelty: Study on projection graphs in the perception of unipotent units is carried out, which is not done earlier in any other algebraic graph.

show abstract

Section: Introductionmentioning

confidence: 99%