In the theory of knowledge graphs, words are represented by word graphs. Sentences are to be represented by sentence graphs. This is called structural parsing. Under consideration of the semantic and syntactic features of natural language, both semantic and syntactic word graphs are formed, the latter expressing the function of word types like nouns, verbs, etc. Traditional grammar rules can be...

Graphs are a powerful data structure that can be applied to several problems in bioinformatics. Graph matching, in its diverse forms, is an important operation on graphs, involved when there is the need to compare two graphs or to find substructures into larger structures. Many graph matching algorithms exist, and their relative efficiency depends on the kinds of graphs they are applied to. In ...

The tenacity of an incomplete connected graph G is defined as T (G) = min{ |S|+m(G−S) ω(G−S) : S ⊂ V (G), ω(G− S) > 1}, where ω(G− S) and m(G− S), respectively, denote the number of components and the order of a largest component inG−S. This is a reasonable parameter to measure the vulnerability of networks, as it takes into account both the amount of work done to damage the network and how bad...

Topoi are known to be categories with extra properties that make them much alike the category of Sets. In a Topoi it is possible to define adequate notions of membership, elements and subobjects, power ”sets”, and finally, every Topoi has an internal logic able to justify any reasoning carried inside it. Most of the cases, this logic is not Classical (Boolean). The general logic for the Topoi i...

Article history: Available online 25 March 2011 Submitted by J.J. Loiseau AMS classification: 15A80 15A39 15A03

In this paper, Nordhaus-Gaddum type relations on open support independence number of some derived graphs path related under addition and multiplication are studied.

Given a set ξ = {H1,H2, · · ·} of connected non acyclic graphs, a ξ-free graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let Ŵk,ξ be theexponential generating function (EGF for brief) of connected ξ-free graphs of excess equal to k (k ≥ 1). For each fixed ξ, a fundamental differen...

Given a set ξ = {H1,H2, · · ·} of connected non acyclic graphs, a ξ-free graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let Ŵk,ξ be theexponential generating function (EGF for brief) of connected ξ-free graphs of excess equal to k (k ≥ 1). For each fixed ξ, a fundamental differen...

distance-balanced graphs are introduced as graphs in which every edge uv has the followingproperty: the number of vertices closer to u than to v is equal to the number of vertices closerto v than to u. basic properties of these graphs are obtained. in this paper, we study theconditions under which some graph operations produce a distance-balanced graph.

A derived graph is a obtained from given according to some predetermined rules. Two of the most frequently used graphs are line and total graph. Calculating properties helps calculate same original For this reason, relations between its always welcomed. recently introduced index which also acts as invariant called omega obtain such for graphs. As an illustrative exercise, values number faces cl...