Even harmonious labelings of disjoint graphs with a small component
A graph G with q edges is said to be harmonious if there is an injection f from the vertices of G to the group of integers modulo q such that when each edge xy is assigned the label f(x)+f(y)(modq), the resulting edge labels are distinct. If G is a tree, exactly one label may be used on two vertices...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2015-11-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0972860015000432 |
| _version_ | 1818112212064010240 |
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| author | Joseph A. Gallian Danielle Stewart |
| author_facet | Joseph A. Gallian Danielle Stewart |
| author_sort | Joseph A. Gallian |
| collection | DOAJ |
| description | A graph G with q edges is said to be harmonious if there is an injection f from the vertices of G to the group of integers modulo q such that when each edge xy is assigned the label f(x)+f(y)(modq), the resulting edge labels are distinct. If G is a tree, exactly one label may be used on two vertices. Over the years, many variations of harmonious labelings have been introduced.
We study a variant of harmonious labeling. A function f is said to be a properly even harmonious labeling of a graph G with q edges if f is an injection from the vertices of G to the integers from 0 to 2(q−1) and the induced function f∗ from the edges of G to 0,2,…,2(q−1) defined by f∗(xy)=f(x)+f(y)(mod2q) is bijective. We investigate the existence of properly even harmonious labelings of families of disconnected graphs with one of C3,C4,K4 or W4 as a component. |
| first_indexed | 2024-12-11T03:15:20Z |
| format | Article |
| id | doaj.art-7cddb9c2e8764511b522c0e46052f486 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 |
| language | English |
| last_indexed | 2024-12-11T03:15:20Z |
| publishDate | 2015-11-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-7cddb9c2e8764511b522c0e46052f4862022-12-22T01:22:46ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002015-11-0112220421510.1016/j.akcej.2015.11.016Even harmonious labelings of disjoint graphs with a small componentJoseph A. GallianDanielle StewartA graph G with q edges is said to be harmonious if there is an injection f from the vertices of G to the group of integers modulo q such that when each edge xy is assigned the label f(x)+f(y)(modq), the resulting edge labels are distinct. If G is a tree, exactly one label may be used on two vertices. Over the years, many variations of harmonious labelings have been introduced. We study a variant of harmonious labeling. A function f is said to be a properly even harmonious labeling of a graph G with q edges if f is an injection from the vertices of G to the integers from 0 to 2(q−1) and the induced function f∗ from the edges of G to 0,2,…,2(q−1) defined by f∗(xy)=f(x)+f(y)(mod2q) is bijective. We investigate the existence of properly even harmonious labelings of families of disconnected graphs with one of C3,C4,K4 or W4 as a component.http://www.sciencedirect.com/science/article/pii/S0972860015000432Properly even harmonious labelingsEven harmonious labelingsHarmonious labelingsGraph labelings |
| spellingShingle | Joseph A. Gallian Danielle Stewart Even harmonious labelings of disjoint graphs with a small component AKCE International Journal of Graphs and Combinatorics Properly even harmonious labelings Even harmonious labelings Harmonious labelings Graph labelings |
| title | Even harmonious labelings of disjoint graphs with a small component |
| title_full | Even harmonious labelings of disjoint graphs with a small component |
| title_fullStr | Even harmonious labelings of disjoint graphs with a small component |
| title_full_unstemmed | Even harmonious labelings of disjoint graphs with a small component |
| title_short | Even harmonious labelings of disjoint graphs with a small component |
| title_sort | even harmonious labelings of disjoint graphs with a small component |
| topic | Properly even harmonious labelings Even harmonious labelings Harmonious labelings Graph labelings |
| url | http://www.sciencedirect.com/science/article/pii/S0972860015000432 |
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