We propose Hilbert transform and analytic signal construction for signals over graphs. This is motivated by the popularity of Hilbert transform, analytic signal, and modulation analysis in conventional signal processing, and the observation that complementary insight is often obtained by viewing conventional signals in the graph setting. Our definitions of Hilbert transform and analytic signal ...

In this paper, we revisit the concept of (normalized) closeness centrality a vertex in graph and investigate it some graphs under operations. Specifically, derive formulas that compute vertices shadow graph, complementary prism, edge corona, disjunction graphs.

Let G(V,X) be a finite and simple graph of order n size m. The complement G, denoted by G¯, is the obtained removing lines G adding that are not in G. A self-complementary if only it isomorphic to its complement. In this paper, we define δ-complement δ′-complement as follows. For any two points u v with degu=degv remove between add which thus called degu≠degv δ(δ′)-self-complementary G≅Gδ(G≅Gδ′...

Abstract The complementary prism $$\Gamma {\bar{\Gamma }}$$ Γ ¯ is constructed from the disjoint union of a graph $$ and its complement $${\bar{\Gamma if an edge added between each pair identical vertices in . It generalizes Petersen graph, whic...

We study the parameterized complexity of the propositional model counting problem #SAT for CNF formulas. As the parameter we consider the treewidth of the following two graphs associated with CNF formulas: the consensus graph and the conflict graph. Both graphs have as vertices the clauses of the formula; in the consensus graph two clauses are adjacent if they do not contain a complementary pai...

This paper addresses the fundamental problem of complex network synchronizability from a graph-theoretic approach. First, the existing results are briefly reviewed. Then, the relationships between the network synchronizability and network structural parameters (e.g., average distance, degree distribution, and node betweenness centrality) are discussed. The effects of the complementary graph of ...

‎In this paper we study codes $C_p(overline{{rm HiS}})$ where $p =3,7‎, ‎11$ defined by the 3‎- ‎7‎- ‎and 11-modular representations of the simple sporadic group ${rm HS}$ of Higman and Sims of degree 100‎. ‎With exception of $p=11$ the codes are those defined by the row span of the adjacency matrix of the complement of the Higman-Sims graph over $GF(3)$ and $GF(7).$ We show that these codes ha...

A graph G = (V,E) is Complementary Distance Pattern Uniform if there exists M ⊂ V (G) such that fM (u) = {d(u, v) : v ∈ M}, for every u ∈ V (G)−M , is independent of the choice of u ∈ V (G)−M and the set M is called the Complementary Distance Pattern Uniform Set (CDPU set). The M -Complementary Distance Uniform Matrix (M CDU Matrix), CM (G) = [cij ] of G of order n is a p × m matrix, where m is...

The biclique partition number (bp) of a graph G is referred to as the least complete bipartite (biclique) subgraphs that are required cover edges exactly once. In this paper, we show co-chordal (complementary chordal) G=(V,E) less than maximal cliques (mc) its complementary graph: A chordal Gc=(V,Ec). We first provide general framework “divide and conquer” heuristic finding minimum partitions g...