On the forgotten topological index of signed graphs
UDC 519.17 The forgotten topological index denoted by $F(G)$ of a graph $G=(V,E)$ is defined as follows: $F(G)=\displaystyle\sum\nolimits_{i=1}^{n}\!d_v^3,$ where $d_v$ denotes the degree of the vertex $v.$ We extend the notion of forgotten topological index to signed graphs and introduce the $MS$...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8298 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1863402191933407232 |
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| author | Pirzada, Shariefuddin Rashid, Mir Riyaz Ul Pirzada, Shariefuddin Rashid, Mir Riyaz Ul |
| author_facet | Pirzada, Shariefuddin Rashid, Mir Riyaz Ul Pirzada, Shariefuddin Rashid, Mir Riyaz Ul |
| author_sort | Pirzada, Shariefuddin |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-04-24T12:38:52Z |
| description | UDC 519.17
The forgotten topological index denoted by $F(G)$ of a graph $G=(V,E)$ is defined as follows: $F(G)=\displaystyle\sum\nolimits_{i=1}^{n}\!d_v^3,$ where $d_v$ denotes the degree of the vertex $v.$ We extend the notion of forgotten topological index to signed graphs and introduce the $MS$-index of a signed graph. Moreover, we determine the forgotten topological index for the tensor product, Cartesian product, lexicographic product, strong product, symmetric difference, and the joint of the graphs $G_1$ and $G_2$ in terms of the forgotten topological index, the first Zagreb index, and the $M\kern-1ptS$-index of signed graphs $\Sigma_1=(G_1,\sigma_1)$ and $\Sigma_2=(G_2,\sigma_2),$ along with their sizes and orders. |
| doi_str_mv | 10.3842/umzh.v78i1-2.8298 |
| first_indexed | 2026-03-24T03:38:02Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8298 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-04-25T01:00:11Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-82982026-04-24T12:38:52Z On the forgotten topological index of signed graphs On the forgotten topological index of signed graphs Pirzada, Shariefuddin Rashid, Mir Riyaz Ul Pirzada, Shariefuddin Rashid, Mir Riyaz Ul Signed graph graph products first Zagreb index $F$-index $MS$-index $Y$-index Signed graph graph products first Zagreb index $F$-index $MS$-index $Y$-index UDC 519.17 The forgotten topological index denoted by $F(G)$ of a graph $G=(V,E)$ is defined as follows: $F(G)=\displaystyle\sum\nolimits_{i=1}^{n}\!d_v^3,$ where $d_v$ denotes the degree of the vertex $v.$ We extend the notion of forgotten topological index to signed graphs and introduce the $MS$-index of a signed graph. Moreover, we determine the forgotten topological index for the tensor product, Cartesian product, lexicographic product, strong product, symmetric difference, and the joint of the graphs $G_1$ and $G_2$ in terms of the forgotten topological index, the first Zagreb index, and the $M\kern-1ptS$-index of signed graphs $\Sigma_1=(G_1,\sigma_1)$ and $\Sigma_2=(G_2,\sigma_2),$ along with their sizes and orders. УДК 519.17 Про забутий топологічний індекс знакових графів Забутий топологічний індекс графа $G=(V,E),$ позначений через $F(G),$ визначено як $F(G)=\displaystyle\sum\nolimits_{i=1}^{n}d_v^3,$ де $d_v$ – степінь вершини $v.$ Розширено поняття забутого топологічного індексу на знакові графи та запроваджено $MS$-індекс знакового графа. Визначено забутий топологічний індекс тензорного добутку, декартового добутку, лексикографічного добутку, сильного добутку, симетричної різниці та об’єднання графів $G_1$ і $G_2$ у термінах забутого топологічного індексу, першого загребського індексу та $M\kern-1ptS$-індексу знакових графів $\Sigma_1=(G_1,\sigma_1)$ і $\Sigma_2=(G_2,\sigma_2),$ а також їхніх розмірів і порядків. Institute of Mathematics, NAS of Ukraine 2026-04-23 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8298 10.3842/umzh.v78i1-2.8298 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 1-2 (2026); 89–90 Український математичний журнал; Том 78 № 1-2 (2026); 89–90 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8298/10627 Copyright (c) 2026 Shariefuddin Pirzada, Mir Riyaz ul Rashid |
| spellingShingle | Pirzada, Shariefuddin Rashid, Mir Riyaz Ul Pirzada, Shariefuddin Rashid, Mir Riyaz Ul On the forgotten topological index of signed graphs |
| title | On the forgotten topological index of signed graphs |
| title_alt | On the forgotten topological index of signed graphs |
| title_full | On the forgotten topological index of signed graphs |
| title_fullStr | On the forgotten topological index of signed graphs |
| title_full_unstemmed | On the forgotten topological index of signed graphs |
| title_short | On the forgotten topological index of signed graphs |
| title_sort | on the forgotten topological index of signed graphs |
| topic_facet | Signed graph graph products first Zagreb index $F$-index $MS$-index $Y$-index Signed graph graph products first Zagreb index $F$-index $MS$-index $Y$-index |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8298 |
| work_keys_str_mv | AT pirzadashariefuddin ontheforgottentopologicalindexofsignedgraphs AT rashidmirriyazul ontheforgottentopologicalindexofsignedgraphs AT pirzadashariefuddin ontheforgottentopologicalindexofsignedgraphs AT rashidmirriyazul ontheforgottentopologicalindexofsignedgraphs |