A product of graphs is a binary operation defined on the class of graphs. Much study has
been done on the adjacency matrix and the Laplacian matrix of graphs. Here, we study the …

In this paper, we define a ternary graph operation which generalizes the construction of
subdivision graph, R-graph, central graph. Also, it generalizes the construction of overlay …

In this article, taking a Fiedler's result on the spectrum of a matrix formed from two symmetric
matrices as a motivation, we deduce a more general result on the eigenvalues of a matrix …

如果存在一种顶点标号, 使得2 个简单图的邻接矩阵可交换, 则称2 个简单图可交换. 首先,
从图的Perron 向量, 主特征值数量, 正则性三方面给出了可交换图的必要条件. 然后 …

In this paper, we explore the concept of the “matrix product of graphs,” initially introduced by
Prasad, Sudhakara, Sujatha, and M. Vinay. This operation involves the multiplication of …

In this paper, we characterize the graphs G and H for which the product of the adjacency
matrices A (G) A (H) is graphical. We continue to define matrix product of two graphs and …

In this paper we consider a graph G, a partition P=[V< sub> 1, V< sub> 2,..., V< sub> k} of V
(G) and the generalized complements G< sub> k< sup> P and G< sub> k (i)< sup> P with …

In this paper, we introduce the notion of perfect matching property for a k-partition of vertex
set of given graph. We consider nontrivial graphs G and GPk, the k-complement of graph G …

In this paper, we obtain the generalized distance spectra and the distance spectra of the
graphs constructed by 2736 and 1588 binary graph operations of the\(\mathcal {M}\)-join …

A matrix with entries 0, 1 is graphical if it is symmetric and all its diagonal entries are zero.
Let G 1, G 2 and G 3 be graphs defined on the same set of vertices. The graph G 3 is said to …