Relationship Between Block Domination Parameters of a Graph

Abstract

Two vertices u, w ∈ V, vv-dominate each other if they are incident on the same block. A set S ⊆ V is a vv-dominating set (VVD-set) if every vertex in V – S is vv-dominated by a vertex in S. The vv-domination number γvv = γvv(G) is the cardinality of a minimum VVD-set of G. Two blocks b1, b2 ∈ B(G) the set of all blocks of G, bb-dominate each other if there is a common cutpoint. A set L ⊆ B(G) is said to be a bb-dominating set (BBD set) if every block in B(G) – L is bb-dominated by some block in L. The bb-domination number γbb = γbb(G) is the cardinality of a minimum BBD-set of G. A vertex v and a block b are said to b-dominate each other if v is incident on the block b. Then vb-domination number γvb = γvb(G) (bv-domination number γbv = γbv(G)) is the minimum number of vertices (blocks) needed to b-dominate all the blocks (vertices) of G. In this paper we study the properties of these block domination parameters and establish a relation between these parameters giving an inequality chain consisting of nine parameters.

Design and analysis of novel structural geometries for piezoresistive pressure sensors allowing improved measurement sensitivity

“…The demand for pressure sensors over a wide range of pressures varying from hundreds of Pa to dozens of MPa and the growing demand for pressure tests in high-temperature environments (>200 °C) have spurred the development of robust and reliable MEMS-based pressure sensor technologies involving silicon, Silicon on Insulator (SOI), Silicon on Sapphire (SOS), Silicon Carbide (SiC) and Carbon Nanotubes (CNT) [Bhat, 2013], [Suja, 2015]. As a result, the wide applications further promote the development of the micro-manufacturing technology.…”

“…It is also easier to place the resistors parallel and perpendicular to the edges of the membrane which are in the <110> direction, thus ensuring that the piezoresistive coefficients π l and π t are maximum along this direction. Figure 2.9 Silicon piezoresistive pressure sensor [Bhat, 2013].…”

“…Therefore, the isolation between the resistors is maintained even at temperatures in excess of 250 °C. Figure 2.10 SOI piezoresistive pressure sensor [Bhat, 2013].…”