Cepheids are the primary distance indicators for extragalactic astronomy and therefore are of very high astrophysical interest. Unfortunately, they are rare stars, situated very far from Earth. Though they are supergiants, their typical angular diameter is only a few milliarcseconds, making them very challenging targets even for long-baseline interferometers. We report observations that were ob...

The betweenness centrality of a vertex of a graph is the portion of shortest paths between all pairs of vertices passing through that vertex. We study selected general properties of this invariant and its relations to distance parameters (diameter, mean distance); also, there are studied properties of graphs whose vertices have the same value of betweenness centrality.

In this paper we study the sequence (ci)0≤i≤d for a distance-regular graph. In particular we show that if d ≥ 2j and cj = c > 1 then c2j > c holds. Using this we give improvements on diameter bounds by Hiraki and Koolen [5], and Pyber [8], respectively, by applying this inequality.

Let denote a bipartite distance-regular graph with diameter D ≥ 4, valency k ≥ 3, and distinct eigenvalues θ0 > θ1 > · · · > θD . Let M denote the Bose-Mesner algebra of . For 0 ≤ i ≤ D, let Ei denote the primitive idempotent of M associated with θi . We refer to E0 and ED as the trivial idempotents of M . Let E, F denote primitive idempotents of M . We say the pair E, F is taut whenever (i) E,...

The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...

We prove the following bound for a k regular graph on n vertices with nontrivial eigenvalues from the interval r s n k rs k r k s Equality holds if and only if the graph is strongly regular with eigenvalues in fk s rg Nonbipartite distance regular graphs with diameter d and eigenvalues k d whose local graphs satisfy the above bound with equality for s b and r b d are called tight graphs and are...

abstract the saturated hydraulic conductivity (ks) is an important physical property of soil. the direct measurement of this property in soils is a difficult and time consuming process. pedotransfer functions (ptfs) provide an alternative by estimating soil parameters from more readily available soil data. the objective of this study is to determine effective factors on soil hydraulic conductiv...