A Memory Constrained Approximate Bayesian Inference Approach Using Incremental Construction of Clique Trees

<div>The complexity of inference using the belief propagation algorithms increases exponentially with the maximum clique size. We describe an approximate inference approach when there are clique size limitations due to memory constraints using incremental construction of clique trees.<br></div>

A Memory Constrained Approximate Bayesian Inference Approach Using Incremental Construction of Clique Trees

<div>The complexity of inference using the belief propagation algorithms increases exponentially with the maximum clique size. We describe an approximate inference approach when there are clique size limitations due to memory constraints using incremental construction of clique trees.<br></div>

On Maximal Distance Energy

Let G be a graph of order n. If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy ED(G) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D(G). In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39.

The Distance Laplacian Spectral Radius of Clique Trees

The distance Laplacian matrix of a connected graph G is defined as ℒ G = Tr G − D G , where D G is the distance matrix of G and Tr G is the diagonal matrix of vertex transmissions of G . The largest eigenvalue of ℒ G is called the distance Laplacian spectral radius of G . In this paper, we determine the graphs with maximum and minimum distance Laplacian spectral radius among all clique trees with n vertices and k cliques. Moreover, we obtain n vertices and k cliques.

Clique Trees of Infinite Locally Finite Chordal Graphs

We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are in bijection with the edges of the corresponding collection of finite trees. This allows us to enumerate the clique trees of a chordal graph and extend various classic characterisations of clique trees to the infinite setting.