12 papers
Extremal graphs for the -th eigenvalue
Hitesh Kumar, Bojan Mohar, Seyed Ahmad Mojallal +1
For a simple graph of order , let denote its adjacency eigenvalues. Hong's problem asks for the optimal upper bound for . A recent theo…
Energy and independence number
Hitesh Kumar, Shivaramakrishna Pragada
For a graph of order , with adjacency eigenvalues , the \emph{energy} of is defined to be \[\mathcal{E}(G)=\sum_{i=1}^{n} |λ_i(G)|.\]…
An improved bound for the strong clique index of graphs
Hitesh Kumar, Bojan Mohar, Shivaramakrishna Pragada
For a graph with line graph , and are called the \emph{strong chromatic index} and \emph{strong clique index} of , respectively. A well-known…
Spectral Radius, Vertex Deletion, and Chromatic Number of Signed Graphs
Abhay Jayarajan, M. Rajesh Kannan, Priti Prasanna Mondal +1
A signed graph is a graph with edges given signs or defined by the function . The adjacency matrix of is defined as per these signs. The relation betw…
Localized Turán-type inequalities for -index
M. Rajesh Kannan, Hitesh Kumar, Shivaramakrishna Pragada
For a connected graph \(G\), let denote the -index of , i.e., the largest eigenvalue of its signless Laplacian matrix. Abreu and Nikiforov (2013) showed that \[ q(G) \…
Maximum spectral sum of graphs
Hitesh Kumar, Lele Liu, Hermie Monterde +2
For a graph of order , the spectral sum of is defined to be the sum , where (resp. ) is the largest (resp. second largest) adjacenc…