6 papers
Extremal Graphs with Prescribed Parameters for the Spectral Radius of Weighted Adjacency Matrices with Property
Swathi Shetty, B. R. Rakshith, Sayinath Udupa N.
In the literature, several graph matrices based on vertex degrees have been introduced, and the study of their spectral properties has attracted considerable attention in recent ye…
Extremal Spectral Radius in Bicyclic and Bipartite Unicyclic Graphs
Swathi Shetty, B. R. Rakshith, Sayinath Udupa N.
The ABS spectral radius of a graph G is defined as the largest eigenvalue of its matrix. Motivated by recent studies on this parameter, in this paper, we determine the bipart…
On extremal graphs with respect to the ABS index
Swathi Shetty, B. R. Rakshith, Sayinath Udupa N.
Recently, Ali et al. posed several open problems concerning extremal graphs with respect to the ABS index. These problems involve characterizing graphs that attain the maximum ABS…
On Coalition Graphs and Coalition Count of Graphs
Swathi Shetty, Sayinath Udupa N. V., B. R. Rakshith
Let be graph with vertex set and order . A coalition in a graph consists of two disjoint sets of vertices and , neither of which is a dominating set bu…
Secure coalitions in graphs
Swathi Shetty, Sayinath Udupa N. V., B. R. Rakshith
A secure coalition in a graph consists of two disjoint vertex sets and , neither of which is a secure dominating set, but whose union forms a secure d…
On the spectrum and energy of graphs
Swathi Shetty, B. R. Rakshith, Sayinath Udupa N.
Let be the eigenavalues of matrix. In this paper, we characterize connected graphs with eigenvalue . As…