# Altitude of wheels and wheel-like graphs

Tomasz Dzido; Hanna Furmańczyk

Open Mathematics (2010)

- Volume: 8, Issue: 2, page 319-326
- ISSN: 2391-5455

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topTomasz Dzido, and Hanna Furmańczyk. "Altitude of wheels and wheel-like graphs." Open Mathematics 8.2 (2010): 319-326. <http://eudml.org/doc/269750>.

@article{TomaszDzido2010,

abstract = {An edge-ordering of a graph G=(V, E) is a one-to-one mapping f:E(G)→\{1, 2, ..., |E(G)|\}. A path of length k in G is called a (k, f)-ascent if f increases along the successive edges forming the path. The altitude α(G) of G is the greatest integer k such that for all edge-orderings f, G has a (k, f)-ascent. In our paper we give exact values of α(G) for all helms and wheels. Furthermore, we use our result to obtain altitude for graphs that are subgraphs of helms.},

author = {Tomasz Dzido, Hanna Furmańczyk},

journal = {Open Mathematics},

keywords = {Altitude; Edge-ordering; Increasing paths; altitude; edge-ordering; increasing paths},

language = {eng},

number = {2},

pages = {319-326},

title = {Altitude of wheels and wheel-like graphs},

url = {http://eudml.org/doc/269750},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Tomasz Dzido

AU - Hanna Furmańczyk

TI - Altitude of wheels and wheel-like graphs

JO - Open Mathematics

PY - 2010

VL - 8

IS - 2

SP - 319

EP - 326

AB - An edge-ordering of a graph G=(V, E) is a one-to-one mapping f:E(G)→{1, 2, ..., |E(G)|}. A path of length k in G is called a (k, f)-ascent if f increases along the successive edges forming the path. The altitude α(G) of G is the greatest integer k such that for all edge-orderings f, G has a (k, f)-ascent. In our paper we give exact values of α(G) for all helms and wheels. Furthermore, we use our result to obtain altitude for graphs that are subgraphs of helms.

LA - eng

KW - Altitude; Edge-ordering; Increasing paths; altitude; edge-ordering; increasing paths

UR - http://eudml.org/doc/269750

ER -

## References

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- [3] Burger A.P., Mynhardt C.M., Clark T.C., Falvai B., Henderson N.D.R., Altitude of regular graphs with girth at least five,Disc. Math.,2005,294,241–257 http://dx.doi.org/10.1016/j.disc.2005.02.007 Zbl1062.05131
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- [6] Katrenič J., Semanišin G., Complexity of ascent finding problem, Proceedings of SOFSEM 2008, High Tatras, Slovakia, January 20–24, 2008, II, 70–77

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