In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$  associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $  C^* $-algebra  $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...

a graph of size n is said to be graceful when is possible toassign distinct integers from {0, 1, . . . , n} to its verticesand {|f(u)−f(v)| : uv ∈ e(g)} consists of n integers. inthis paper we present broader families of graceful graphs; these families are obtained via three different operations: the third power of a caterpillar, the symmetric product of g and k2 , and the disjoint :union: of g...

The connective constant of a graph is the exponential growth rate of the number of self-avoiding walks starting at a given vertex. Strict inequalities are proved for connective constants of vertex-transitive graphs. First, the connective constant decreases strictly when the graph is replaced by a nontrivial quotient graph. Second, the connective constant increases strictly when a quasitransitiv...

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...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

Tel-Aviv University 1.1 The elimination tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 The elimination game • The elimination tree data structure • An algorithm • A skeleton graph • Supernodes 1.2 Applications of etrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8 Efficient symbolic factorization • Predicting row and column nonzero counts •...

Given a periodic graph, we wish to determine via combinatorial methods whether it has embeddings in the plane that—via motions that preserve edge-lengths and periodicity—can be continuously deformed into another non-congruent embedding of graph. By introducing NBAC-colourings for corresponding quotient gain graphs, identify which graphs have flexible when lattice periodicity is fixed. We furthe...

DNA nanoarchitechtures require carefully designed oligonucleotides with certain non-hybridization guarantees, which can be formalized as the q-uniqueness property on the sequence level. We study the optimization problem of finding a longest q-unique DNA sequence. We first present a convenient formulation as an integer linear program on the underlying De Bruijn graph that allows to flexibly inco...

For a partial cube (that is, an isometric subgraph of a hypercube) G, quotient graphs G, G , and G∼ have the equivalence classes of the DjokovićWinkler relation as the vertex set, while edges are defined in three different natural ways. Several results on these quotients are proved and the concepts are compared. For instance, for every graph G there exists a median graphM such that G = M τ . Tr...

Let Γ be a group acting without inversions on a tree X. If there is no proper Γ-invariant subtree, we call the action of Γ on X minimal. Here we give a characterization of non-minimal tree actions. For a non-minimal action of Γ on X, we give structure theorems for the quotient graph of groups for Γ on X, its associated edge-indexed graph and its group of deck transformations.