the stability of a communication network composed of processing nodes and communication links is of prime importance to network designers. as the network begins losing links or nodes, eventually there is a loss in its effectiveness. thus, communication networks must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible...

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

Using a generalised version of Gershgorin's circle theorem, rigorous boundaries on the energies lowest states broad class line graphs above critical filling are derived for hardcore bosonic systems. Also lower boundary energy gap towards next is established. Additionally, it shown that corresponding eigenstates dominated by subspace spanned containing compactly localised pair and overlap as wel...

In this paper we unify several existing regularity conditions for graphs, including strong regularity, k-isoregularity, and the t-vertex condition. We develop an algebraic composition/decomposition theory of conditions. Using our theoretical results show that a family non rank 3 graphs known to satisfy 7-vertex condition fulfills even stronger condition, (3,7)-regularity (the notion is defined ...

We propose a new approach to text semantic analysis and general corpus using, as termed in this article, "bi-gram graph" representation of corpus. The different attributes derived from graph theory are measured analyzed unique insights or against other graphs. observe vast domain tools algorithms that can be developed on top the representation; creating such proves computationally cheap, much h...

Let $$\gamma (G)$$ and _{t}(G)$$ be the domination number total of a graph G, respectively, let _g(G)$$ _{tg}(G)$$ game respectively. Then, G is _g$$ -perfect (resp. _{tg}$$ -perfect) if every induced subgraph F satisfies _g(F)=\gamma (F)$$ _{tg}(F)=\gamma _t(F)$$ ). A recursive characterization graphs derived. The yields polynomial recognition algorithm for graphs. It proved that minimally -im...

We investigate combinatorial and algebraic aspects of the interplay between renormalization monodromies for Feynman amplitudes. clarify how extraction subgraphs from a graph interacts with putting edges onshell or contracting them to obtain reduced graphs. Graph by this leads study cointeracting bialgebras. One bialgebra comes hence is needed renormalization. The other an incidence put either o...

in this paper, the degree distance and the gutman index of the corona product of two graphs are determined. using the results obtained, the exact degree distance and gutman index of certain classes of graphs are computed.

General versions of Kalman filtering and recursive least-squares algorithms are derived as instances of the sum(mary)-product algorithm on Forney-style factor graphs.

In the companion paper [Linear rank-width of distance-hereditary graphs I. A polynomialtime algorithm, Algorithmica 78(1):342–377, 2017], we presented a characterization of the linear rank-width of distance-hereditary graphs, from which we derived an algorithm to compute it in polynomial time. In this paper, we investigate structural properties of distance-hereditary graphs based on this charac...