Related papers: Adjacency Energy of Hypergraphs
We prove that, for any graph $G$, its graph energy is at least twice the Randic index. We show that equality holds if and only if $G$ is the union of complete bipartite graphs.
An $r$-uniform supertree is a connected and acyclic hypergraph of which each edge has $r$ vertices, where $r\geq 3$. We propose the concept of matching energy for an $r$-uniform hypergraph, which is defined as the sum of the absolute value…
In this paper we develop the concept of energy of a vertex introduced in Arizmendi and Juarez-Romero (2016). We derive basic inequalities, continuity properties, give examples and extend the definition to locally finite graphs.
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
For a simple graph $G$, the energy $\mathcal{E}(G)$ is defined as the sum of the absolute values of all the eigenvalues of its adjacency matrix $A(G)$. Let $n, m$, respectively, be the number of vertices and edges of $G$. One well-known…
Motivated by the linear time algorithm that locates the eigenvalues of a cograph G [10], we investigate the multiplicity of eigenvalue for \lambda \neq -1,0. For cographs with balanced cotrees we determine explicitly the highest value for…
In this paper, we consider the Randi\'{c} energy $RE$ of simple connected graphs. We provide upper bounds for $RE$ in terms of the number of vertices and the nullity of the graph. We present families of graphs that satisfy the Conjecture…
Circulant graphs are an important class of interconnection networks in parallel and distributed computing. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer as well. The…
We analyze graphs attaining the extreme values of various spectral indices in the class of all simple connected graphs, as well as in the class of graphs which are not complete multipartite graphs. We also present results on density of…
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
This note answers extremal questions like: what is the maximum number of edges in a graph of order n, which belongs to some hereditary property. The same question is answered also for the spectral radius and other similar parameters.
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
Let $\G$ be an oriented graph of order $n$ and $\a_1,\a_2,..., \a_n$ denote all the eigenvalues of the skew-adjacency matrix of $\G.$ The skew energy $\displaystyle{\cal E}_s(\G)= \sum_{i=1}^{n} |\a_i|.$ In this paper, the oriented…
The energy of a graph $G$ is the sum of the absolute values of the eigenvalues of the adjacency matrix of $G$. Let $s^+(G), s^-(G)$ denote the sum of the squares of the positive and negative eigenvalues of $G$, respectively. It was…
The $f$ adjacency matrix is a type of edge-weighted adjacency matrix, whose weight of an edge $ij$ is $f(d_i,d_j)$, where $f$ is a real symmetric function and $d_i,d_j$ are the degrees of vertex $i$ and vertex $j$. The $f$-spectral radius…
The local properties problem of Erd\H{o}s and Shelah generalizes many Ramsey problems and some distinct distances problems. In this work, we derive a variety of new bounds for the local properties problem and its variants. We do this by…
The energy of a graph is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. In this paper, we characterize the tetracyclic graph of order $n$ with minimal energy. By this, the validity of a conjecture for…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…
The energy $E(G)$ of a graph $G$ is defined as the sum of the absolute values of its eigenvalues. Let $S_2$ be the star of order 2 (or $K_2$) and $Q$ be the graph obtained from $S_2$ by attaching two pendent edges to each of the end…