Related papers: On sign-symmetric signed graphs
A split graph is a graph whose vertices can be partitioned into a clique and a stable set. We investigate the combinatorial species of split graphs, providing species-theoretic generalizations of enumerative results due to B\'ina and…
A graph $G$ is called \emph{symmetric with respect to a functional $F_G(P)$} defined on the set of all the probability distributions on its vertex set if the distribution $P^*$ maximizing $F_G(P)$ is uniform on $V(G)$. Using the…
We investigate a class of 2-edge coloured bipartite graphs known as alternating signed bipartite graphs (ASBGs) that encode the information in alternating sign matrices. The central question is when a given bipartite graph admits an…
The set D of distinct signed degrees of the vertices in a signed graph G is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed…
A signed graph is a pair $(G,\Sigma)$, where $G=(V,E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V={1,...,n}$ and $\Sigma\subseteq E$. By $S(G,\Sigma)$ we denote the set of all symmetric $V\times V$…
Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric…
There are many concepts of signed graph coloring which are defined by assigning colors to the vertices of the graphs. These concepts usually differ in the number of self-inverse colors used. We introduce a unifying concept for this kind of…
A weighted graph $G^{\omega}$ consists of a simple graph $G$ with a weight $\omega$, which is a mapping,$\omega$: $E(G)\rightarrow\mathbb{Z}\backslash\{0\}$. A signed graph is a graph whose edges are labeled with $-1$ or $1$. In this paper,…
Construction of non-isomorphic cospectral graphs is a nontrivial problem in spectral graph theory specially for large graphs. In this paper, we establish that graph theoretical partial transpose of a graph is a potential tool to create…
An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…
A biased graph is a graph $G$, together with a distinguished subset $\mathcal{B}$ of its cycles so that no Theta-subgraph of $G$ contains precisely two cycles in $\mathcal{B}$. A large number of biased graphs can be constructed by choosing…
To each permutation $\sigma$ in $S_{n}$ we associate a triangulation of a fixed $(n+2)$-gon. We then determine the fibers of this association and show that they coincide with the sylvester classes depicted By Novelli, Hivert and Thibon. A…
We prove that for every pair of quantum isomorphic graphs, their block trees and their block graphs are isomorphic, and that such an isomorphism can be chosen so that the corresponding blocks are quantum isomorphic -- in particular,…
We consider symmetric powers of a graph. In particular, we show that the spectra of the symmetric square of strongly regular graphs with the same parameters are equal. We also provide some bounds on the spectra of the symmetric squares of…
A hypermap is (hypervertex-) bipartite if its hypervertices can be 2-coloured in such a way that ``neighbouring'' hypervertices have different colours. It is bipartite-uniform if within each of the sets of hypervertices of the same colour,…
We study homomorphism problems of signed graphs from a computational point of view. A signed graph $(G,\Sigma)$ is a graph $G$ where each edge is given a sign, positive or negative; $\Sigma\subseteq E(G)$ denotes the set of negative edges.…
In this paper, we define the Mycielskian of a signed graph and discuss the properties of balance and switching in the Mycielskian of a given signed graph. We provide a condition for ensuring the Mycielskian of a balanced signed graph…
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)]. They appear to be the most natural choice for the spectral…
Intuitively speaking, a bipartite graph is mirror if it can be drawn in the Cartesian plane in such a way that, the vertices of one stable are points in x=0, the vertices of the other stable set are points in x=1, the edges are straight…
Let $S$ be a set of transpositions generating the symmetric group $S_n$. The transposition graph of $S$ is defined to be the graph with vertex set $\{1,\ldots,n\}$, and with vertices $i$ and $j$ being adjacent in $T(S)$ whenever $(i,j) \in…