Chromatic Zagreb indices for graphical embodiment of colour clusters
<p>For a colour cluster <span class="math"><em>C</em> = (C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub>, …, C<sub>ℓ</sub>)</span>, where <span class="math">C<sub><em>i</em></sub&...
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| Format: | Article |
| Language: | English |
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InaCombS; Universitas Jember; dan Universitas Indonesia
2019-06-01
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| Series: | Indonesian Journal of Combinatorics |
| Subjects: | |
| Online Access: | http://www.ijc.or.id/index.php/ijc/article/view/44 |
| _version_ | 1819277142359277568 |
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| author | Johan Kok Sudev Naduvath Muhammad Kamran Jamil |
| author_facet | Johan Kok Sudev Naduvath Muhammad Kamran Jamil |
| author_sort | Johan Kok |
| collection | DOAJ |
| description | <p>For a colour cluster <span class="math"><em>C</em> = (C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub>, …, C<sub>ℓ</sub>)</span>, where <span class="math">C<sub><em>i</em></sub></span> is a colour class such that <span class="math">∣C<sub><em>i</em></sub>∣ = <em>r</em><sub><em>i</em></sub></span>, a positive integer, we investigate two types of simple connected graph structures <span class="math"><em>G</em><sub>1</sub><sup><em>C</em></sup></span>, <span class="math"><em>G</em><sub>2</sub><sup><em>C</em></sup></span> which represent graphical embodiments of the colour cluster such that the chromatic numbers <span class="math"><em>χ</em>(<em>G</em><sub>1</sub><sup><em>C</em></sup>) = <em>χ</em>(<em>G</em><sub>2</sub><sup><em>C</em></sup>) = ℓ</span> and <span class="math">$\min\{\varepsilon(G^{C}_1)\}=\min\{\varepsilon(G^{C}_2)\} =\sum\limits_{i=1}^{\ell}r_i-1$</span>, and <span class="math"><em>ɛ</em>(<em>G</em>)</span> is the size of a graph <span class="math"><em>G</em></span>. In this paper, we also discuss the chromatic Zagreb indices corresponding to <span class="math"><em>G</em><sub>1</sub><sup><em>C</em></sup></span>, <span class="math"><em>G</em><sub>2</sub><sup><em>C</em></sup></span>.</p> |
| first_indexed | 2024-12-23T23:51:25Z |
| format | Article |
| id | doaj.art-578be54b1ae24896a028864cc7f9b5e5 |
| institution | Directory Open Access Journal |
| issn | 2541-2205 |
| language | English |
| last_indexed | 2024-12-23T23:51:25Z |
| publishDate | 2019-06-01 |
| publisher | InaCombS; Universitas Jember; dan Universitas Indonesia |
| record_format | Article |
| series | Indonesian Journal of Combinatorics |
| spelling | doaj.art-578be54b1ae24896a028864cc7f9b5e52022-12-21T17:25:23ZengInaCombS; Universitas Jember; dan Universitas IndonesiaIndonesian Journal of Combinatorics2541-22052019-06-0131486210.19184/ijc.2019.3.1.629Chromatic Zagreb indices for graphical embodiment of colour clustersJohan Kok0Sudev Naduvath1Muhammad Kamran Jamil2CHRIST (Deemed to be University) BangaloreVidya Academy of Science & Technology Thrissur, Kerala, India.Riphah International University, Lahore<p>For a colour cluster <span class="math"><em>C</em> = (C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub>, …, C<sub>ℓ</sub>)</span>, where <span class="math">C<sub><em>i</em></sub></span> is a colour class such that <span class="math">∣C<sub><em>i</em></sub>∣ = <em>r</em><sub><em>i</em></sub></span>, a positive integer, we investigate two types of simple connected graph structures <span class="math"><em>G</em><sub>1</sub><sup><em>C</em></sup></span>, <span class="math"><em>G</em><sub>2</sub><sup><em>C</em></sup></span> which represent graphical embodiments of the colour cluster such that the chromatic numbers <span class="math"><em>χ</em>(<em>G</em><sub>1</sub><sup><em>C</em></sup>) = <em>χ</em>(<em>G</em><sub>2</sub><sup><em>C</em></sup>) = ℓ</span> and <span class="math">$\min\{\varepsilon(G^{C}_1)\}=\min\{\varepsilon(G^{C}_2)\} =\sum\limits_{i=1}^{\ell}r_i-1$</span>, and <span class="math"><em>ɛ</em>(<em>G</em>)</span> is the size of a graph <span class="math"><em>G</em></span>. In this paper, we also discuss the chromatic Zagreb indices corresponding to <span class="math"><em>G</em><sub>1</sub><sup><em>C</em></sup></span>, <span class="math"><em>G</em><sub>2</sub><sup><em>C</em></sup></span>.</p>http://www.ijc.or.id/index.php/ijc/article/view/44graphical embodimentscolour clusterscolour classeschromatic zagreb indices. |
| spellingShingle | Johan Kok Sudev Naduvath Muhammad Kamran Jamil Chromatic Zagreb indices for graphical embodiment of colour clusters Indonesian Journal of Combinatorics graphical embodiments colour clusters colour classes chromatic zagreb indices. |
| title | Chromatic Zagreb indices for graphical embodiment of colour clusters |
| title_full | Chromatic Zagreb indices for graphical embodiment of colour clusters |
| title_fullStr | Chromatic Zagreb indices for graphical embodiment of colour clusters |
| title_full_unstemmed | Chromatic Zagreb indices for graphical embodiment of colour clusters |
| title_short | Chromatic Zagreb indices for graphical embodiment of colour clusters |
| title_sort | chromatic zagreb indices for graphical embodiment of colour clusters |
| topic | graphical embodiments colour clusters colour classes chromatic zagreb indices. |
| url | http://www.ijc.or.id/index.php/ijc/article/view/44 |
| work_keys_str_mv | AT johankok chromaticzagrebindicesforgraphicalembodimentofcolourclusters AT sudevnaduvath chromaticzagrebindicesforgraphicalembodimentofcolourclusters AT muhammadkamranjamil chromaticzagrebindicesforgraphicalembodimentofcolourclusters |