Related papers: Signless Laplacian State Transfer on Vertex Comple…

A fractional matching of a graph $G$ is a function $f$ giving each edge a number in $[0,1]$ such that $\sum_{e\in\Gamma(v)}f(e)\leq1$ for each vertex $v\in V(G)$, where $\Gamma(v)$ is the set of edges incident to $v$. The fractional…

A signed graph $S=(G, \sigma)$ is a pair in which $G$ is an underlying graph and $\sigma$ is a function from the edge set to $\{\pm1\}$. For signed graphs $S_{1}$ and $S_{2}$ on $n_{1}$ and $n_{2}$ vertices, respectively, the signed…

A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in…

A continuous-time quantum random walk describes the motion of a quantum mechanical particle on an underlying graph. The graph itself is associated with a Hilbert space of dimension equal to the number of vertices. The dynamics of the walk…

In this paper, we extend our earlier proposal of corona product of signed graphs into generalized corona product of signed graphs inspired by the generalized corona product of unsigned graphs. Then we study structural balance and spectral…

In this paper, we study pretty good state transfer (PGST) in Grover walks on graphs. We consider transfer of quantum states that are localized at the vertices of a graph and we use Chebyshev polynomials to analyze PGST between such states.…

We consider the representation of a continuous-time quantum walk in a graph $X$ by the matrix $\exp(itA(X))$. We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to…

A cover of a graph $G$ is a graph $H$ with vertex set $V(H) = \bigcup_{v \in V(G)} L_{v}$, where $L_{v} = \{v\} \times [s]$, and the edge set $M = \bigcup_{uv \in E(G)} M_{uv}$, where $M_{uv}$ is a matching between $L_{u}$ and $L_{v}$. A…

Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement…

Representing graphs as quantum states is becoming an increasingly important approach to study entanglement of mixed states, alternate to the standard linear algebraic density matrix-based approach of study. In this paper, we propose a…

The distance signless Laplacian matrix of a graph $G$ is define as $Q(G)=$Tr$(G)+D(G)$, where Tr$(G)$ and $D(G)$ are the diagonal matrix of vertex transmissions and the distance matrix of $G$, respectively. Denote by $E_G(v)$ the set of all…

\noindent A perfect dominating set in a graph $G=(V,E)$ is a subset $S \subseteq V$ such that each vertex in $V \setminus S$ has exactly one neighbor in $S$. A perfect coalition in $G$ consists of two disjoint sets of vertices $V_i$ and…

We characterize perfect state transfer on real-weighted graphs of the Johnson scheme $\mathcal{J}(n,k)$. Given $\mathcal{J}(n,k)=\{A_1, A_2, \cdots, A_k\}$ and $A(X) = w_0A_0 + \cdots + w_m A_m$, we show, using classical number theory…

{Signless Laplacian determinations of some graphs with independent edges}% {Let $G$ be a simple undirected graph. Then the signless Laplacian matrix of $G$ is defined as $D_G + A_G$ in which $D_G$ and $A_G$ denote the degree matrix and the…

In this paper, we show that for a graph of order $n$, where $n\ge 5$, if the signless Laplacian index is larger than or equal to certain value depending on $n$, then the graph contains a doubly chorded cycle, where the chords incident to a…

A vertex in a graph is said to be sedentary if a quantum state assigned on that vertex tends to stay on that vertex. Under mild conditions, we show that the direct product and join operations preserve vertex sedentariness. We also…

Given a graph $G$, a subset $S \subseteq V(G)$ is \textit{cycle convex}, if for any vertex $v \in V(G) \setminus S$, the induced subgraph, $G[S \cup \{v\}]$ cannot form a cycle containing the vertex $v$. The \textit{exchange number} of $G$,…

Let $G$ be an edge-colored graph, a walk in $G$ is said to be a properly colored walk iff each pair of consecutive edges have different colors, including the first and the last edges in case that the walk be closed. Let $H$ be a graph…

The minimum number of total independent partition sets of $V \cup E$ of a graph $G=(V,E)$ is called the \emph{total chromatic number} of $G$, denoted by $\chi''(G)$. If the difference between cardinalities of any two total independent sets…

A simple method for transmitting quantum states within a quantum computer is via a quantum spin chain---that is, a path on $n$ vertices. Unweighted paths are of limited use, and so a natural generalization is to consider weighted paths;…