We consider simulations of graph automata. We introduce two local transformations on the neighborhood: splitting and merging. We explain how to use such transformations, and their consequences on the topology of the simulated graph, the speed of the simulation and the memory size of simulating automata in some cases. As an example , we apply these transformations to graph automata embedded on s...

Let M be a closed orientable 3-manifold of Heegaard genus two with a non-trivial JSJ-decomposition and G be a finite group of orientation-preserving smooth actions on M which preserves each handlebody of Heegaard splitting and each piece of the JSJ-decomposition of M . We will call some specific conditions of the Heegaard splitting and the JSJ-tori the condition A, . . . , and the condition F. ...

A JSJ-splitting of a group G over a certain class of subgroups is a graph of groups decomposition of G which describes all possible decompositions of G as an amalgamated product or an HNN extension over subgroups lying in the given class. Such decompositions originated in 3-manifold topology. In this paper we generalize the JSJ-splitting constructions of Sela, Rips-Sela and Dunwoody-Sageev and ...

A JSJ-splitting of a group G over a certain class of subgroups is a graph of groups decomposition of G which describes all possible decompositions of G as an amalgamated product or an HNN extension over subgroups lying in the given class. Such decompositions originated in 3-manifold topology. In this paper we generalize the JSJ-splitting constructions of Sela, Rips–Sela and Dunwoody–Sageev, and...

a concept related to the spectrum of a graph is that of energy. the energy e(g) of a graph g is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of g . the laplacian energy of a graph g is equal to the sum of distances of the laplacian eigenvalues of g and the average degree d(g) of g. in this paper we introduce the concept of laplacian energy of fuzzy graphs. ...

In this paper, we obtain a forbidden-minor characterization of the class of binary gammoids M such that, for every pair of elements x, y of M, both the splitting matroid Mx,y and the element splitting matroid M ′ x,y are binary gammoids.

In recent work, thermal energy gaps. AE, it °PUPS gas, Ana; Gibbs free energy gaps, AG.,, between singlet(s) and triplet 0) states of 5.12C3H2C, I m (4 N. P. As and Sb) were calculated and compared with thoseanalogues. MC2113C, (M= CIL N. P. As and Sb) at B3LYIE6-311-NG" level of theory. Our itself showedthat Gibbs free energy gaps. AG, for l uu and 1 p are less than IS and I's, respectively. I...

a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.

We investigate 2-planarizing 2-factors, i.e. 2-factors of embedded graphs so that cutting along the cycles 2-factor we get two plane where are a spanning set face boundaries in each graphs. will give necessary criteria for an abstract graph to have embedding with as well such 2-factor. Along way, discuss which degree classical results from planar hamiltonicity theory can be extended our framewo...

The families of Edge Intersection Graphs of Paths in a tree (resp. in a grid) EPT (resp. EPG) are well studied graph classes. Recently we introduced the class of graphs of Edge-Intersecting and NonSplitting Paths in a Tree (ENPT) [2]. In this model, two vertices are adjacent if they represent two intersecting paths of a tree whose union is also a path. In this study we generalize this graph cla...