Let R be a ring with non-zero identity.The unit graph of R,denoted by G(R),is an undirected graph with all the elements of R as vertices and where distinct vertices x,y are adjacent if and only if x+y is a unit of R.I...Let R be a ring with non-zero identity.The unit graph of R,denoted by G(R),is an undirected graph with all the elements of R as vertices and where distinct vertices x,y are adjacent if and only if x+y is a unit of R.In this paper,we investigate the Wiener index and hyper-Wiener index of G(R)and explicitly determine their values.展开更多
基金supported in part by a grant from Science and Engineering Research Board,India(Ref.MTR/2017/000830)supported by the National Natural Science Foundation of China(Ref.11961050)the Guangxi Natural Sciences Foundation(Ref.2021GXNSFAA220043).
文摘Let R be a ring with non-zero identity.The unit graph of R,denoted by G(R),is an undirected graph with all the elements of R as vertices and where distinct vertices x,y are adjacent if and only if x+y is a unit of R.In this paper,we investigate the Wiener index and hyper-Wiener index of G(R)and explicitly determine their values.
