It is known that the problem of computing adjacency dimension a graph NP-hard. This suggests finding for special classes graphs or obtaining good bounds on this invariant. In work we obtain general G in terms parameters . We discuss tightness these and, some particular graphs, closed formulae. particular, show close relationships exist between and other parameters, like domination number, locat...

Felsner, Li and Trotter showed that the dimension of adjacency poset an outerplanar graph is at most 5, gave example whose has 4. We improve their upper bound to 4, which then best possible.

Recently, Huang showed that every ( 2 n − 1 + ) -vertex induced subgraph of the n-dimensional hypercube has maximum degree at least . In this paper, we discuss subgraphs Cartesian product graphs and semistrong to generalize Huang's result. Let Γ be a connected signed bipartite graph order m. By defining two kinds , denoted by □ ˜ ⋈ show if have exactly distinct adjacency eigenvalues ± θ respect...

Let −→ G be a digraph and A( −→ G) be the adjacency matrix of −→ G . Let D( −→ G) be the diagonal matrix with outdegrees of vertices of −→ G and Q( −→ G) = D( −→ G) + A( −→ G) be the signless Laplacian matrix of −→ G . The spectral radius of Q( −→ G) is called the signless Laplacian spectral radius of −→ G . In this paper, we determine the unique digraph which attains the maximum (or minimum) s...

In this paper, we show that the dimension of the adjacency poset of a planar graph is at most 8. From below, we show that there is a planar graph whose adjacency poset has dimension 5. We then show that the dimension of the adjacency poset of an outerplanar graph is at most 5. From below, we show that there is an outerplanar graph whose adjacency poset has dimension 4. We also show that the dim...

In this paper we will apply the tensor and its traces to investigate spectral characterization of unicyclic graphs. Let $G$ be a graph $G^m$ $m$-th power (hypergraph) $G$. The spectrum is referring adjacency matrix, tensor. called determined by high-ordered spectra (DHS for short) if, whenever $H$ such that $H^m$ cospectral with all $m$, then isomorphic first give formulas graphs, provide some ...

Let G be a graph with n vertices and m edges. The degree sequence of G is denoted by d1 ≥ d2 ≥ · · · ≥ dn. Let A(G) and D(G) = diag(di : 1 ≤ i ≤ n) be the adjacency matrix and the degree diagonal matrix of G, respectively. The Laplacian matrix of G is L(G) = D(G) − A(G). It is well known that L(G) is a symmetric, semidefinite matrix. We assume the spectrum of L(G), or the Laplacian spectrum of ...