in this paper we define the removable cycle that, if $im$ is a class of graphs, $gin im$, the cycle $c$ in $g$ is called removable if $g-e(c)in im$. the removable cycles in eulerian graphs have been studied. we characterize eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for eulerian graph to have removable cycles h...

We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras $L(E)$ $L(F)$ of graphs $E$ $F$ over a commutative ground ring $\ell$. approach this by studying structure such under bivariant algebraic $K$-theory $kk$, which is universal theory with properties above. show that very mild assumptions on $\ell$, ...

We prove that if $G=(V,E)$ is an $\omega$-stable (respectively, superstable) graph with $\chi (G)>\aleph _0$ $2^{\aleph _0}$) then $G$ contains all the finite subgraphs of shift $\mathrm {Sh}_n(\omega )$ for some $n$. a variant this theorem graphs interpretable in stationary stable theories. Furthermore, $\operatorname {U}(G)\leq 2$ we $n\leq suffices.

Finding clusters of well-connected nodes in a graph is a problem common to many domains, including social networks, the Internet and bioinformatics. From a computational viewpoint, finding these clusters or graph communities is a difficult problem. We use a clique matrix decomposition based on a statistical description that encourages clusters to be well connected and few in number. The formal ...

We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the...

Communication games are crucial tools for investigating the limitations of physical theories. The communication complexity (CC) problem is a typical example, which several distributed parties attempt to jointly calculate given function with limited classical communications. In this work, we present method construct CC problems from Bell tests in graph-theoretic way. Starting an experimental com...

altan derivatives of polycyclic conjugated hydrocarbons were recently introduced and studied in theoretical organic chemistry. we now provide a generalization of the altan concept, applicable to any graph. several earlier noticed topological properties of altan derivatives of polycyclic conjugated hydrocarbons are shown to be the properties of all altan derivatives of all graphs. among these ar...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

In this paper, we study the asymptotics of the degree sequence of permutation graphs associated with a sequence of random permutations. The limiting finite-dimensional distributions of the degree proportions are established using results from graph and permutation limit theories. In particular, we show that for a uniform random permutation, the joint distribution of the degree proportions of th...

In the analysis of the structure of totally categorical first order theories, the second author showed that certain combinatorial counting functions play an important role. Those functions are invariants of the structures and are always polynomials in one or many variables, depending on the number of independent dimensions of the theory in question. The first author introduced the notion of gra...