# On graphs with a unique minimum hull set

Discussiones Mathematicae Graph Theory (2001)

- Volume: 21, Issue: 1, page 31-42
- ISSN: 2083-5892

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topGary Chartrand, and Ping Zhang. "On graphs with a unique minimum hull set." Discussiones Mathematicae Graph Theory 21.1 (2001): 31-42. <http://eudml.org/doc/270467>.

@article{GaryChartrand2001,

abstract = {We show that for every integer k ≥ 2 and every k graphs G₁,G₂,...,Gₖ, there exists a hull graph with k hull vertices v₁,v₂,...,vₖ such that link $L(v_i) = G_i$ for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a,b of integers with a ≥ 2 and b ≥ 0 is realizable as the hull number and forcing geodetic number of a hull graph.},

author = {Gary Chartrand, Ping Zhang},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {geodetic set; geodetic number; convex hull; hull set; hull number; hull graph},

language = {eng},

number = {1},

pages = {31-42},

title = {On graphs with a unique minimum hull set},

url = {http://eudml.org/doc/270467},

volume = {21},

year = {2001},

}

TY - JOUR

AU - Gary Chartrand

AU - Ping Zhang

TI - On graphs with a unique minimum hull set

JO - Discussiones Mathematicae Graph Theory

PY - 2001

VL - 21

IS - 1

SP - 31

EP - 42

AB - We show that for every integer k ≥ 2 and every k graphs G₁,G₂,...,Gₖ, there exists a hull graph with k hull vertices v₁,v₂,...,vₖ such that link $L(v_i) = G_i$ for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a,b of integers with a ≥ 2 and b ≥ 0 is realizable as the hull number and forcing geodetic number of a hull graph.

LA - eng

KW - geodetic set; geodetic number; convex hull; hull set; hull number; hull graph

UR - http://eudml.org/doc/270467

ER -

## References

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