{"title":"彩色萨格勒布指数的彩色集群的图形体现","authors":"J. Kok, S. Naduvath, M. Jamil","doi":"10.19184/IJC.2019.3.1.6","DOIUrl":null,"url":null,"abstract":"<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>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"112 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Chromatic Zagreb indices for graphical embodiment of colour clusters\",\"authors\":\"J. Kok, S. Naduvath, M. Jamil\",\"doi\":\"10.19184/IJC.2019.3.1.6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<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>\",\"PeriodicalId\":13506,\"journal\":{\"name\":\"Indonesian Journal of Combinatorics\",\"volume\":\"112 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indonesian Journal of Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.19184/IJC.2019.3.1.6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indonesian Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19184/IJC.2019.3.1.6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Chromatic Zagreb indices for graphical embodiment of colour clusters
For a colour cluster C = (C1, C2, C3, …, Cℓ), where Ci is a colour class such that ∣Ci∣ = ri, a positive integer, we investigate two types of simple connected graph structures G1C, G2C which represent graphical embodiments of the colour cluster such that the chromatic numbers χ(G1C) = χ(G2C) = ℓ and $\min\{\varepsilon(G^{C}_1)\}=\min\{\varepsilon(G^{C}_2)\} =\sum\limits_{i=1}^{\ell}r_i-1$, and ɛ(G) is the size of a graph G. In this paper, we also discuss the chromatic Zagreb indices corresponding to G1C, G2C.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
