Related papers: Constructing cospectral graphs via regular rationa…

The search for a highly discriminating and easily computable invariant to distinguish graphs remains a challenging research topic. Here we focus on cospectral graphs whose complements are also cospectral (generalized cospectral), and on…

Let $p, k, q$ be positive integers with $p-2 \geqslant k$ and let $K_{p,k}^{q}$ be the generalized pineapple graph which is obtained by joining independent set of $q$ vertices with $k$ vertices of a complete graph $K_{p}.$ In \cite{TSH2},…

A threshold graph G on n vertices is defined by binary sequence of length n. In this paper we present an explicit formula for computing the characteristic polynomial of a threshold graph from its binary sequence. Applications include…

In a recent series of papers, Hosoya drew the attention to a particular aspect of constructing cospectral graphs by using coalescences: that cospectral graphs can be constructed by attaching multiple copies of a rooted graph in different…

Local operations of combinatorial structures (graphs, Hadamard matrices, codes, designs) that maintain the basic parameters unaltered, have been widely used in the literature under the name of switching. We show an equivalence between two…

For an $n$-vertex graph $G$ with adjacency matrix $A$, the walk matrix $W(G)$ of $G$ is the matrix $[e,Ae,\ldots,A^{n-1}e]$, where $e$ is the all-ones vector. Suppose that $W(G)$ is nonsingular and $p$ is an odd prime such that $W(G)$ has…

Two graphs are said to be $Q$-cospectral if they share the same signless Laplacian spectrum. A simple graph is said to be determined by its signless Laplacian spectrum (abbreviated as DQS) if there exists no other non-isomorphic simple…

Two simple undirected graphs are cospectral if their respective adjacency matrices have the same multiset of eigenvalues. Cospectrality yields an equivalence relation on the family of graphs which is provably weaker than isomorphism. In…

Assumed to be undirected, simple, and connected are all of the graphs in this study, and adjacency matrix $A$ serves as the associated matrix. In this paper we show that it is possible to relate a creation sequence for a type of cographs…

Given a quantum graph $ \Gamma $, a finite symmetry group $ G $ acting on it and a representation $ R $ of $ G $, the quotient quantum graph $ \Gamma /R $ is described and constructed in the literature [1, 2, 18]. In particular, it was…

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…

Coalescing involves gluing one or more rooted graphs onto another graph. Under specific conditions, it is possible to start with cospectral graphs that are coalesced in similar ways that will result in new cospectral graphs. We present a…

We consider matrices of the form $qD+A$, with $D$ being the diagonal matrix of degrees, $A$ being the adjacency matrix, and $q$ a fixed value. Given a graph $H$ and $B\subseteq V(G)$, which we call a coalescent pair $(H,B)$, we derive a…

It is well known that the spectrum and the Smith normal form of a matrix can be computed in polynomial time. Thus, it is interesting to explore how good are these parameters for distinguishing graphs. This is relevant since it is related to…

The spectrum of the $k$-power hypergraph of a graph $G$ is called the $k$-ordered spectrum of $G$.If graphs $G_1$ and $G_2$ have same $k$-ordered spectrum for all positive integer $k\geq2$, $G_1$ and $G_2$ are said to be high-ordered…

We present a construction of Neumaier graphs with nexus 1, which generalises two known constructions of Neumaier graphs. We also use W. Wang, L. Qiu, and Y. Hu switching to show that we construct cospectral Neumaier graphs. Finally, we show…

Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…

Let $\Gamma=(G,\sigma)$ be a signed graph, where $\sigma$ is the sign function on the edges of $G$. In this paper, we use the operation of partial transpose to obtain non-isomorphic Laplacian cospectral signed graphs. We will introduce two…

In this article, we propose a new type of square matrix associated with an undirected graph by trading off the naturally imbedded symmetry in them. The proposed matrix is defined using the neighbourhood sets of the vertices. It is called as…

Let $G$ be a simple, connected graph and let $A(G)$ be the adjacency matrix of $G$. If $D(G)$ is the diagonal matrix of the vertex degrees of $G$, then for every real $\alpha \in [0,1]$, the matrix $A_{\alpha}(G)$ is defined as…