The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a “transmission” system. A transmission system is a mathematical representation of a means of transmitting (multi-parameter) data along directed edges from vertex to vertex. The associated transmission graph Laplacian is shown to have many of the former properties of the classica...

In this paper, we study the square of generalized Hamming graphs by properties abelian groups, and characterize some isomorphisms between non-complete extended p-sum complete graphs. As applications, determine eigenvalues

• Let G be a graph. For subset X of V ( ), the switching σ is signed graph obtained from by reversing signs all edges between and ) ∖ . A( adjacency matrix An eigenvalue called main if it has an eigenvector sum whose entries not equal to zero. Two equivalent graphs share same spectrum, while they may have different eigenvalues. Akbari et al. (2021) conjectured that let ≠ K 2 , 4 { e } Then ther...

We study partially distance-regular graphs and partially walkregular graphs as generalizations of distance-regular graphs and walkregular graphs respectively. We conclude that the partially distanceregular graphs can be viewed as some extremal graphs of partially walk-regular graphs. In the special case that the graph is assumed to be regular with four distinct eigenvalues, a well known class o...