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…
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…
Bounds on the Inverse symmetric division deg index and the relation with other topological indices of graphs
Kinkar Chandra Das, B. R. Rakshith, Wojciech Macek
Let be a simple graph. The concept of Inverse symmetric division deg index was introduced in the chemical graph theory very recently. In spite of this, a few pap…
On Energy of Graphs with Self-Loops
B. R. Rakshith, Kinkar Chandra Das, B. J. Manjunatha
Let G be a simple graph on n vertices with vertex set V(G). The energy of G, denoted by, is the sum of all absolute values of the eigenvalues of the adjacency matr…