Computing optimal assignments for residual network reliability
Discrete Applied Mathematics
An algorithm for the Tutte polynomials of graphs of bounded treewidth
Discrete Mathematics
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Graphs determined by polynomial invariants
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width
Combinatorics, Probability and Computing
A Subset Expansion of the Coloured Tutte Polynomial
Combinatorics, Probability and Computing
On Graphs Determined by Their Tutte Polynomials
Graphs and Combinatorics
The interlace polynomial of a graph
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
From a Zoo to a Zoology: Towards a General Theory of Graph Polynomials
Theory of Computing Systems
A Most General Edge Elimination Polynomial
Graph-Theoretic Concepts in Computer Science
An extension of the bivariate chromatic polynomial
European Journal of Combinatorics
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Note: On the colored Tutte polynomial of a graph of bounded treewidth
Discrete Applied Mathematics
A Most General Edge Elimination Polynomial - Thickening of Edges
Fundamenta Informaticae - Bridging Logic and Computer Science: to Johann A. Makowsky for his 60th birthday
Linear recurrence relations for graph polynomials
Pillars of computer science
Complexity of the Bollobás-Riordan polynomial: exceptional points and uniform reductions
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
From a zoo to a zoology: descriptive complexity for graph polynomials
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Approximating rank-width and clique-width quickly
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Journal of Logic and Computation
Complexity of the cover polynomial
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
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Inspired by the study of community structure in connection networks, we introduce the graph polynomial Q(G;x,y), the bivariate generating function which counts the number of connected components in induced subgraphs. We give a recursive definition of Q(G;x,y) using vertex deletion, vertex contraction and deletion of a vertex together with its neighborhood and prove a universality property. We relate Q(G;x,y) to other known graph invariants and graph polynomials, among them partition functions, the Tutte polynomial, the independence and matching polynomials, and the universal edge elimination polynomial introduced by I. Averbouch et al. (2008) [5]. We show that Q(G;x,y) is vertex reconstructible in the sense of Kelly and Ulam, and discuss its use in computing residual connectedness reliability. Finally we show that the computation of Q(G;x,y) is @?P-hard, but fixed parameter tractable for graphs of bounded tree-width and clique-width.