Odd Harmonious Labeling of Some Classes of Graphs
A graph $G(p,q)$ is said to be odd harmonious if there exists an injection $f: V(G)\rightarrow\left\{0, 1, 2,\cdots,2q-1\right\}$ such that the induced function $f^{*}: E(G)\rightarrow\left\{1, 3,\cdots,2q-1\right\}$ defined by $f^{*}(uv) = f(u)+ f(v)$ is a bijection. In this paper we prove that $T_...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Universidad de La Frontera
2020-12-01
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| Series: | Cubo |
| Subjects: | |
| Online Access: | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2466/2023 |
| _version_ | 1818412528960536576 |
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| author | P. Jeyanthi S. Philo |
| author_facet | P. Jeyanthi S. Philo |
| author_sort | P. Jeyanthi |
| collection | DOAJ |
| description | A graph $G(p,q)$ is said to be odd harmonious if there exists an injection $f: V(G)\rightarrow\left\{0, 1, 2,\cdots,2q-1\right\}$ such that the induced function $f^{*}: E(G)\rightarrow\left\{1, 3,\cdots,2q-1\right\}$ defined by $f^{*}(uv) = f(u)+ f(v)$ is a bijection. In this paper we prove that $T_p$- tree, $T\hat\circ P_m$, $T\hat\circ 2P_m$, regular bamboo tree, $C_n\hat\circ P_m$, $C_n\hat\circ 2P_m$ and subdivided grid graphs are odd harmonious. |
| first_indexed | 2024-12-14T10:48:45Z |
| format | Article |
| id | doaj.art-507421582834463395fc1f0969807f39 |
| institution | Directory Open Access Journal |
| issn | 0716-7776 0719-0646 |
| language | English |
| last_indexed | 2024-12-14T10:48:45Z |
| publishDate | 2020-12-01 |
| publisher | Universidad de La Frontera |
| record_format | Article |
| series | Cubo |
| spelling | doaj.art-507421582834463395fc1f0969807f392022-12-21T23:05:20ZengUniversidad de La FronteraCubo0716-77760719-06462020-12-0122329931410.4067/S0719-06462020000300299Odd Harmonious Labeling of Some Classes of GraphsP. Jeyanthi0https://orcid.org/0000-0003-4349-164XS. Philo1Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur - 628 215, Tamil Nadu, India.Department of Mathematics, St. Xavier’s College, Palayamkottai, Tirunelveli -627002, Tamilnadu, India.A graph $G(p,q)$ is said to be odd harmonious if there exists an injection $f: V(G)\rightarrow\left\{0, 1, 2,\cdots,2q-1\right\}$ such that the induced function $f^{*}: E(G)\rightarrow\left\{1, 3,\cdots,2q-1\right\}$ defined by $f^{*}(uv) = f(u)+ f(v)$ is a bijection. In this paper we prove that $T_p$- tree, $T\hat\circ P_m$, $T\hat\circ 2P_m$, regular bamboo tree, $C_n\hat\circ P_m$, $C_n\hat\circ 2P_m$ and subdivided grid graphs are odd harmonious.http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2466/2023harmonious labelingodd harmonious labelingtransformed treesubdivided grid graphregular bamboo tree |
| spellingShingle | P. Jeyanthi S. Philo Odd Harmonious Labeling of Some Classes of Graphs Cubo harmonious labeling odd harmonious labeling transformed tree subdivided grid graph regular bamboo tree |
| title | Odd Harmonious Labeling of Some Classes of Graphs |
| title_full | Odd Harmonious Labeling of Some Classes of Graphs |
| title_fullStr | Odd Harmonious Labeling of Some Classes of Graphs |
| title_full_unstemmed | Odd Harmonious Labeling of Some Classes of Graphs |
| title_short | Odd Harmonious Labeling of Some Classes of Graphs |
| title_sort | odd harmonious labeling of some classes of graphs |
| topic | harmonious labeling odd harmonious labeling transformed tree subdivided grid graph regular bamboo tree |
| url | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2466/2023 |
| work_keys_str_mv | AT pjeyanthi oddharmoniouslabelingofsomeclassesofgraphs AT sphilo oddharmoniouslabelingofsomeclassesofgraphs |