Transitional Values of Graphs

M.A. Johnson introduced a way to describe a chemical transformation by labeling each vertex and edge of a graph G with one of integers - 1, 0, 1. The labeling of G so obtained is called a transitional labeling of G. The value of a transitional labeling of G is defined as the minimum of the number of...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 34; no. 11; pp. 65 - 79
Main Author Hevia, H.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.1997
Subjects
Applied graph theory
Distances in graphs
Labelings
Mathematical chemistry
Mathematical chemistry
Distances in graphs
Applied graph theory
Labelings
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Summary:M.A. Johnson introduced a way to describe a chemical transformation by labeling each vertex and edge of a graph G with one of integers - 1, 0, 1. The labeling of G so obtained is called a transitional labeling of G. The value of a transitional labeling of G is defined as the minimum of the number of negative elements of G and the number of positive elements of G. We introduce a new invariant of a graph G called the transitional value of G, defined as the maximum value among all the values of the transitional labelings of G. This parameter provides a measure of the structural changes that occur in a chemical transformation represented by a transitional labeling of G. We determine the transitional values of some families of graphs and characterize the transitional labelings of maximum value of complete graphs.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0898-1221
1873-7668
DOI:10.1016/S0898-1221(97)00220-4