For a graph G of order n with adjacency eigenvalues lambda_1(G)>= ...>= lambda_n(G), the cospectrality of G within the set G of all graphs of order n is the smallest spectral distance from G to another graph of G. Abdollahi and Zakeri conjectured that for every n>= 4 the cospectrality of the complete tripartite graph K...
Irena M. Jovanović, Jelena Sedlar, R. Škrekovski· 0 citations
An edge of a multigraph is rich with respect to a proper edge-coloring if all the edges adjacent to it receive mutually distinct colors, and a proper edge-coloring is a rich-neighbor coloring if every non-isolated edge has a rich edge adjacent to it. The least number of colors in such a coloring is the rich-neighbor ch...
Masaki Kashima, M. Petruševski, Jelena Sedlar et al.· 0 citations
Let $\lambda_1(G) \geq \dots \geq \lambda_n(G)$ be the adjacency spectrum of a graph $G$ on $n$ vertices. The spectral distance $\sigma(G,H)$ between $n$-vertex graphs $G$ and $H$ is the Manhattan distance between their spectra, i.e. $\sigma(G,H) = \sum_{i=1}^n |\lambda_i(G) - \lambda_i(H)|$. Given a set $\mathcal{G}$...
Irena M. Jovanović, Jelena Sedlar, R. Škrekovski· 0 citations
A set S of vertices of a graph is odd independent if it is independent and every vertex outside S has either zero or an odd number of neighbors in S. The largest size of such a set is the odd independence number alpha_od. Caro, Petrusevski, Skrekovski and Tuza [2] conjectured that alpha_od = 1 for every finite Queen gr...
M. Knor, Jelena Sedlar, R. Škrekovski· 0 citations
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