2 research outputs found
The extremal problems on the inertia of weighted bicyclic graphs
Let be a weighted graph. The number of the positive, negative and zero
eigenvalues in the spectrum of are called positive inertia index,
negative inertia index and nullity of , and denoted by ,
, , respectively. In this paper, sharp lower bound on
the positive (resp. negative) inertia index of weighted bicyclic graphs of
order with pendant vertices is obtained. Moreover, all the weighted
bicyclic graphs of order with at most two positive, two negative and at
least zero eigenvalues are identified, respectively.Comment: 12 pages, 5 figures, 2 tables. arXiv admin note: text overlap with
arXiv:1307.0059 by other author