For a graph G, we show a theorem that establishes a correspondence between the fine Hilbert series of the Stanley-Reisner ring of the clique complex for the complementary graph of G and the fine subgraph polynomial of G. We obtain from this theorem some corollaries regarding the independent set complex and the matching complex.

A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S = (G,σ) (S = (G,μ)), where G = (V, E) is a graph called the underlying graph of S and σ : E → (e1, e2, · · · , ek) (μ : V → (e1, e2, · · · , ek)) is a function, where each ei ∈ {+,−}. Particularly, a Smarandachely 2-singed graph or 2-marked graph is called abbreviated to a singed graph or a marked graph. We chara...

Many applications involve matching two graphs in order to identify their common features and compute their similarity. In this paper, we address the problem of computing a graph similarity measure based on a multivalent graph matching and which is generic in the sense that other well known graph similarity measures can be viewed as special cases of it. We propose and compare two different kinds...

Chemoinformatics is a well established research field concerned with the discovery of molecule’s properties through informational techniques. Computer science’s research fields mainly concerned by the chemoinformatics field are machine learning and graph theory. From this point of view, graph kernels provide a nice framework combining machine learning techniques with graph theory. Such kernels ...

Hierarchical Control Flow Graph Models deene a modeling paradigm for discrete event simulation modeling based upon hierarchical extensions to Control Flow Graph Models. Conceptually, models consist of a set of encapsulated, concurrently operating model components that interact solely via message passing. The primary objectives of Hierarchical Control Flow Graph Models are: (1) to facilitate mod...

Let G be a non-bipartite strongly regular graph on n vertices of valency k. We prove that if G has a distance-regular antipodal cover of diameter 4, then k ≤ 2(n + 1)/5 , unless G is the complement of triangular graph T (7), the folded Johnson graph J (8, 4) or the folded halved 8-cube. However, for these three graphs the bound k ≤ (n − 1)/2 holds. This result implies that only one of a complem...

A graph G = (V,E) is called to be Smarandachely uniform k-graph for an integer k ≥ 1 if there exists M1,M2, · · · ,Mk ⊂ V (G) such that fMi(u) = {d(u, v) : v ∈ Mi} for ∀u ∈ V (G)−Mi is independent of the choice of u ∈ V (G)−Mi and integer i, 1 ≤ i ≤ k. Each such set Mi, 1 ≤ i ≤ k is called a CDPU set [6, 7]. Particularly, for k = 1, a Smarandachely uniform 1-graph is abbreviated to a complement...

It is provet d that, given any positive integer k, there exists a self-complementary graph with more than 4 .2 4 k vertices which contains no complete subgraph with k+1 vertices . An application of this result to coding theory is mentioned . A graph will be called s-good if it contains neither a complete subgraph with more than s vertices nor an independent set of more than s vertices . A speci...

This paper deals with a universal coding problem for a certain kind of multiterminal source coding system that we call the complementary delivery coding system. Both fixed-to-fixed length and fixed-to-variable length lossless coding schemes are considered. Explicit constructions of universal codes and bounds of the error probabilities are clarified via type-theoretical and graph-theoretical ana...

Popular public knowledge graphs like DBpedia or YAGO are created from Wikipedia as a source, and thus limited to the information contained therein. At the same time, Wikifarms like Fandom contain Wikis for specific topics, which are often complementary to the information contained in Wikipedia. In this paper, we show how the DBpedia approach can be transferred to Fandom to create DBkWik, a comp...