9 papers · 1 filter
Orthogonal signed graphs of degree 5
Maxwell Levit, Bojan Mohar, Behruz Tayfeh-Rezaie
An orthogonal signed graph is a connected signed graph whose signed adjacency matrix has pairwise orthogonal rows. They are closely related to Hadamard matrices, maximal arrangemen…
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…
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 c…
2-cell embeddings of cubic graphs I. The unstable dual
MacKenzie Carr, Bojan Mohar
In this paper, the first of a two-part series, we explore 2-cell embeddings of cubic graphs, particularly those with small genus. Using local rotations, we introduce a new way of d…
Convex combination of first and second eigenvalues of trees
Hitesh Kumar, Bojan Mohar, Shivaramakrishna Pragada +1
For a graph , let and denote the largest and the second largest adjacency eigenvalue of . The sum is called the \emph{spectral sum} of …
Spectrally symmetric orientations of graphs
Saieed Akbari, Jonathan Aloni, Maxwell Levit +2
The Hermitian adjacency matrices of digraphs based on the sixth root of unity were introduced in [B. Mohar, A new kind of Hermitian matrices for digraphs, Linear Alg. Appl. (2020)]…