All posts under category "Computer Science / Discrete Mathematics"
The complexity of dual basis of a type I optimal normal basis of $mathbb{F}_{q^n}$ over $mathbb{F}_{q}$ was determined to be $3n-3$ or $3n-2$ according as $q$ is even or odd, respectively, by Z.-X. Wan and K. Zhou in 2007. We give a new proof to this result by clearly deriving the dual of a type I o
The walk distances in graphs are defined as the result of appropriate transformations of the $sum_{k=0}^infty(tA)^k$ proximity measures, where $A$ is the weighted adjacency matrix of a connected weighted graph and $t$ is a sufficiently small positive parameter. The walk distances are graph-geodetic,
The independence number of a graph G, denoted by alpha(G), is the cardinality of an independent set of maximum size in G, while mu(G) is the size of a maximum matching in G, i.e., its matching number. G is a Konig-Egervary graph if its order equals alpha(G)+mu(G). In this paper we give a new charact
The Turan bound is a famous result in graph theory, which relates the independence number of an undirected graph to its edge density. Also the Caro-Wei inequality, which gives a more refined bound in terms of the vertex degree sequence of a graph, might be regarded today as a classical result. We sh
In this paper, we prove that most of the boolean functions, $f : {-1,1}^n rightarrow {-1,1}$ satisfy the Fourier Entropy Influence (FEI) Conjecture due to Friedgut and Kalai (Proc. AMS'96). The conjecture says that the Entropy of a boolean function is at most a constant times the Influence of the fu
We show that P2T - the problem of deciding whether the edge set of a simple graph can be partitioned into two trees or not - is NP-complete.
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