Unique Metro Domination of a Ladder

A dominating set D of a graph G which is also a resolving set of G is called a metro dominating set. A metro dominating set D of a graph G(V,E) is a unique metro dominating set (in short an UMD-set) if |N(v) \cap D| = 1 for each vertex v in V-D and the minimum cardinality of an UMD-set of G is the unique metro domination number of G. In this paper, we determine unique metro domination number of P_n\times P_2

Unique Metro Domination Number of Circulant Graphs

In this paper, we determine unique metro domination number of circulant graphs

On Classes of Neighborhood Resolving Sets of a Graph

Let G=(V,E) be a simple connected graph. A subset S of V is called a neighbourhood set of G if G=\bigcup_{s\in S}<N[s]>, where N[v] denotes the closed neighbourhood of the vertex v in G. Further for each ordered subset S={s_1,s_2, ...,s_k} of V and a vertex $u\in V$, we associate a vector $\Gamma(u/S)=(d(u,s_1),d(u,s_2), ...,d(u,s_k))$ with respect to S, where d(u,v) denote the distance between u and v in G. A subset S is said to be resolving set of G if $\Gamma(u/S)\neq \Gamma(v/S)$ for all $u,v\in V-S$. A neighbouring set of G which is also a resolving set for G is called a neighbourhood resolving set (nr-set). The purpose of this paper is to introduce various types of nr-sets and compute minimum cardinality of each set, in possible cases, particulary for paths and cycles

Open Neighborhood Coloring of Prisms

For a simple, connected, undirected graph G(V, E) an open neighborhood coloring of the graph G is a mapping f : V (G) --&gt; Z+ such that for each w in V(G), and for all u, v in N(w), f(u) is different from f(v). The maximum value of f(w), for all w in V (G) is called the span of the open neighborhood coloring f. The minimum value of span of f over all open neighborhood colorings f is called open neighborhood chromatic number of G, denoted by Xonc(G). In this paper we determine the open neighborhood chromatic number of prisms

Graphs of Neighborhood Metric Dimension Two

A subset  of vertices of a simple connected graph is a neighborhood set (n-set) of  G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x,y of G, there is a vertex s∈ S such that d(s,x)≠d(s,y). An n-set that serves as a resolving set for G is called an nr-set of G. The nr-set with least cardinality is called an nr-metric basis of G and its cardinality is called the neighborhood metric dimension of graph G. In this paper, we characterize graphs of neighborhood metric dimension two

On the Metric Dimension of Cartesian Products of Graphs

A set S of vertices in a graph G resolves G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. This paper studies the metric dimension of cartesian products G*H. We prove that the metric dimension of G*G is tied in a strong sense to the minimum order of a so-called doubly resolving set in G. Using bounds on the order of doubly resolving sets, we establish bounds on G*H for many examples of G and H. One of our main results is a family of graphs G with bounded metric dimension for which the metric dimension of G*G is unbounded

Role of dutasteride in pre‐clinical ETS fusion‐positive prostate cancer models

BACKGROUND Androgens play a crucial role in prostate cancer, hence the androgenic pathway has become an important target of therapeutic intervention. Previously we discovered that gene fusions between the 5′‐untranslated region of androgen regulated gene TMPRSS2 and the ETS transcription factor family members were present in a majority of the prostate cancer cases. The resulting aberrant overexpression of ETS genes drives tumor progression. METHODS Here, we evaluated the expression levels of 5α‐reductase isoenzymes in prostate cancer cell lines and tissues. We tested the effect of dutasteride, a 5α‐reductase inhibitor, in TMPRSS2–ERG fusion‐positive VCaP cell proliferation and cell invasion. We also evaluated the effect of dutasteride on the TMPRSS2–ERG fusion gene expression. Finally, we tested dutasteride alone or in combination with an anti‐androgen in VCaP cell xenografts tumor model. RESULTS Our data showed that 5α‐reductase SRD5A1 and SRD5A3 isoenzymes that are responsible for the conversion of testosterone to DHT, are highly expressed in metastatic prostate cancer compared to benign and localized prostate cancer. Dutasteride treatment attenuated VCaP cell proliferation and invasion. VCaP cells pre‐treated with dutasteride showed a reduction in ERG and PSA expression. In vivo studies demonstrated that dutasteride in combination with the anti‐androgen bicalutamide significantly decreased tumor burden in VCaP cell xenograft model. CONCLUSIONS Our findings suggest that dutasteride can inhibit ERG fusion‐positive cell growth and in combination with anti‐androgen, significantly reduce the tumor burden. Our study suggests that anti‐androgens used in combination with dutasteride could synergistically augment the therapeutic efficacy in the treatment of ETS‐positive prostate cancer. Prostate 72:1542–1549, 2012. © 2012 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/93574/1/22509_ftp.pd

Whole-Exome Sequencing Reveals High Mutational Concordance between Primary and Matched Recurrent Triple-Negative Breast Cancers

PURPOSE Triple-negative breast cancer (TNBC) is a molecularly complex and heterogeneous breast cancer subtype with distinct biological features and clinical behavior. Although TNBC is associated with an increased risk of metastasis and recurrence, the molecular mechanisms underlying TNBC metastasis remain unclear. We performed whole-exome sequencing (WES) analysis of primary TNBC and paired recurrent tumors to investigate the genetic profile of TNBC. METHODS Genomic DNA extracted from 35 formalin-fixed paraffin-embedded tissue samples from 26 TNBC patients was subjected to WES. Of these, 15 were primary tumors that did not have recurrence, and 11 were primary tumors that had recurrence (nine paired primary and recurrent tumors). Tumors were analyzed for single-nucleotide variants and insertions/deletions. RESULTS The tumor mutational burden (TMB) was 7.6 variants/megabase in primary tumors that recurred (n = 9); 8.2 variants/megabase in corresponding recurrent tumors (n = 9); and 7.3 variants/megabase in primary tumors that did not recur (n = 15). MUC3A was the most frequently mutated gene in all groups. Mutations in MAP3K1 and MUC16 were more common in our dataset. No alterations in PI3KCA were detected in our dataset. CONCLUSIONS We found similar mutational profiles between primary and paired recurrent tumors, suggesting that genomic features may be retained during local recurrence

Role and regulation of coordinately expressed de novo purine biosynthetic enzymes PPAT and PAICS in lung cancer.

Cancer cells exhibit altered metabolism including aerobic glycolysis that channels several glycolytic intermediates into de novo purine biosynthetic pathway. We discovered increased expression of phosphoribosyl amidotransferase (PPAT) and phosphoribosylaminoimidazole carboxylase, phosphoribosylaminoimidazole succinocarboxamide synthetase (PAICS) enzymes of de novo purine biosynthetic pathway in lung adenocarcinomas. Transcript analyses from next-generation RNA sequencing and gene expression profiling studies suggested that PPAT and PAICS can serve as prognostic biomarkers for aggressive lung adenocarcinoma. Immunohistochemical analysis of PAICS performed on tissue microarrays showed increased expression with disease progression and was significantly associated with poor prognosis. Through gene knockdown and over-expression studies we demonstrate that altering PPAT and PAICS expression modulates pyruvate kinase activity, cell proliferation and invasion. Furthermore we identified genomic amplification and aneuploidy of the divergently transcribed PPAT-PAICS genomic region in a subset of lung cancers. We also present evidence for regulation of both PPAT and PAICS and pyruvate kinase activity by L-glutamine, a co-substrate for PPAT. A glutamine antagonist, 6-Diazo-5-oxo-L-norleucine (DON) blocked glutamine mediated induction of PPAT and PAICS as well as reduced pyruvate kinase activity. In summary, this study reveals the regulatory mechanisms by which purine biosynthetic pathway enzymes PPAT and PAICS, and pyruvate kinase activity is increased and exposes an existing metabolic vulnerability in lung cancer cells that can be explored for pharmacological intervention