On the profile of the corona of two graphs |
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| Authors: | Yung-Ling Lai |
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| Affiliation: | a Graduate Institute of Computer Science and Information Engineering, National Chia-Yi University, Chiayi, Taiwan
b Department of Mathematics, National Taiwan University, Taipei 106, Taiwan |
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| Abstract: | The concept of profile, together with bandwidth, originates from handling sparse matrices in solving linear systems of equations. Given a graph G, the profile minimization problem is to find a one-to-one mapping f:V(G)→{1,2,…,|V(G)|} such that ∑v∈V(G)maxx∈Nv](f(v)−f(x)) is as small as possible, where Nv]={v}∪{x:x is adjacent to v}. This paper studies the profile of the corona G∧H of two graphs G and H. In particular, bounds for the profile of the corona of two graphs are established. Also, exact values of the profiles of coronas G∧H are obtained when G has certain properties, including when G is a caterpillar, a complete graph or a cycle. |
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| Keywords: | Profile Corona Numbering Interval graph Caterpillar Complete graph Cycle |
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