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A (undirected) graph is locally irregular if no two of its adjacent vertices have the same degree. A decomposition of a graph G into k locally irregular subgraphs is a partition $E_1,\cdots ,E_k$ of E(G) into k parts each of which induces a locally ...$\mathrm{}\mathrm{}$$\mathrm{}$

The signless Laplacian Estrada index of a graph G is defined as S L E E ( G ) = ∑ i = 1 n e q i, where q 1 , q 2 , … , q n are the eigenvalues of the signless Laplacian matrix of G. A k-tree is either a complete graph on k vertices or a graph ...

Graph pebbling is a network model for transporting discrete resources that are consumed in transit. Deciding whether a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter two graphs, and deciding ...

In this paper we provide a systematic treatment of several shape parameters of (random) k-trees. Our research is motivated by many important algorithmic applications of k-trees in the context of tree-decomposition of a graph and graphs of bounded tree-...

Self-assembly is a process in which simple objects autonomously combine themselves into larger objects. It is considered as a promising technique in nano-technology. Two simple graphs G1 and G2 with a clique of same size overlap and a new self-assembled ...

For a connected graph, a subset of vertices of least size whose deletion increases the number of connected components is the vertex connectivity of the graph. A graph with vertex connectivity k is said to be k-vertex connected. Given a k-vertex ...

For a connected graph, a subset of vertices of least size whose deletion increases the number of connected components is the vertex connectivity of the graph. A graph with vertex connectivity k is said to be k-vertex connected. Given a k-vertex ...

We show that k-tree isomorphism can be decided in logarithmic space by giving a logspace canonical labeling algorithm. This improves over the previous StUL upper bound and matches the lower bound. As a consequence, the isomorphism, the automorphism, as ...

A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential attachment and ...

An approach for factoring general boolean functions was described in Golumbic and Mintz [Factoring logic functions using graph partitioning, in: Proceedings of IEEE/ACM International Conference on Computer Aided Design, November 1999, pp. 195-198] and ...

An approach for factoring general boolean functions was described in Golumbic and Mintz [Factoring logic functions using graph partitioning, in: Proceedings of IEEE/ACM International Conference on Computer Aided Design, November 1999, pp. 195-198] and ...

A k-tree is either a complete graph on k vertices or a graph G=(V,E) that contains a vertex whose neighbourhood in G induces a complete graph on k vertices and whose removal results in a k-tree. We present two new subclasses of k-trees and their ...

A k-tree is either a complete graph on k vertices or a graph G = (V, E) that contains a vertex whose neighbourhood in G induces a complete graph on k vertices and whose removal results in a k-tree. We present two new subclasses of k-trees and their ...

In the feedback vertex set problem, the aim is to minimize, in a connected graph G = (V, E), the cardinality of the set V(G) ⊆ V, whose removal induces an acyclic subgraph. In this paper, we show an interesting relationship between the minimum feedback ...

For each pair of nonadjacent vertices in a graph, consider the greater of the degrees of the two vertices. The minimum of these maxima is a lower bound on the treewidth of a graph, unless it is a complete graph. This bound has three consequences. First, ...

Dynamic programming has long been established as an important technique for demonstrating the existence of polynomial time algorithms for various discrete optimization problems. In this paper we extend the normal paradigm of dynamic programming to allow a ...

A k-tree is a graph that can be reduced to the k-complete graph by a sequence of removals of a degree k vertex with completely connected neighbors. We address the problem of determining whether a graph is a partial graph of a k-tree. This problem is ...

Our interest in the class of k-trees and their partial graphs and subgraphs is motivated by some practical questions about the reliability of communication networks in the presence of constrained line- and site-failures, and about the complexity of ...