On Graphs Having no Flow Roots in the Interval $(1,2)$

On Graphs Having no Flow Roots in the Interval $(1, 2)$

For any graphG, letW (G) be the set of vertices inG of degrees larger than 3. We show that for any bridgeless graph G, if W (G) is dominated by some component of G−W (G), then F (G,λ) has no roots in (1, 2), where F (G,λ) is the flow polynomial of G. This result generalizes the known result that F (G,λ) has no roots in (1, 2) whenever |W (G)| 6 2. We also give some constructions to generate gra...

On planar and non-planar graphs having no chromatic zeros in the interval (1, 2)

We exhibit a family of 2-connected graphs which is closed under certain operations, and show that each graph in the family has no chromatic zeros in the interval (1,2). The family contains not only collections of graphs having no certain minors, but also collections of plane graphs, including near-triangulations found by Birkhoff and Lewis [Chromatic polynomials, Trans. Amer. Math. Soc. 60 (194...

the effects of changing roughness on the flow structure in the bends

flow in natural river bends is a complex and turbulent phenomenon which affects the scour and sedimentations and causes an irregular bed topography on the bed. for the reason, the flow hydralics and the parameters which affect the flow to be studied and understand. in this study the effect of bed and wall roughness using the software fluent discussed in a sharp 90-degree flume bend with 40.3cm ...

On group Elements Having Square Roots

Extremal graphs having no matching cuts

A graph G = (V, E) is matching immune if there is no matching cut in G. We show that for any matching immune graph G, |E| ≥ ⌈3(|V | − 1)/2⌉. This bound is tight, as we define operations that construct, from a given vertex, exactly the class of matching immune graphs that attain the bound.