On derived t-path, t=2,3 signed graph and t-distance signed graph
A signed graph Σ is a pair Σ=(Σu,σ)that consists of a graph (Σu,E) and a sign mapping called signature σ from E to the sign group {+,−}. In this paper, we discuss the t-path product signed graph (Σ)^twhere vertex set of (Σ)^t is the same as that of Σ and two vertices are adjacent if there is a path...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-06-01
|
| Series: | MethodsX |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2215016125000081 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832592822344089600 |
|---|---|
| author | Deepa Sinha Sachin Somra |
| author_facet | Deepa Sinha Sachin Somra |
| author_sort | Deepa Sinha |
| collection | DOAJ |
| description | A signed graph Σ is a pair Σ=(Σu,σ)that consists of a graph (Σu,E) and a sign mapping called signature σ from E to the sign group {+,−}. In this paper, we discuss the t-path product signed graph (Σ)^twhere vertex set of (Σ)^t is the same as that of Σ and two vertices are adjacent if there is a path of length t, between them in the signed graph Σ. The sign of an edge in the t-path product signed graph is determined by the product of marks of the vertices in the signed graph Σ, where the mark of a vertex is the product of signs of all edges incident to it. In this paper, we provide a characterization of Σ which are switching equivalent to t-path product signed graphs (Σ)^t for t=2,3 which are switching equivalent to Σ and also the negation of the signed graph ŋ(Σ) that are switching equivalent to (Σ)^t for t=2,3. We also characterize signed graphs that are switching equivalent to t-distance signed graph (Σ¯)t for t=2 where 2-distance signed graph (Σ¯)2=(V′,E′,σ′) defined as follows: the vertex set is same as the original signed graph Σ and two vertices u,v∈(Σ¯)2, are adjacent if and only if there exists a distance of length two in Σ. The edge uv∈(Σ¯)2 is negative if and only if all the edges, in all the distances of length two in Σ are negative otherwise the edge is positive. The t-path network along with these characterizations can be used to develop model for the study of various real life problems communication networks. • t-path product signed graph. • t-distance signed graph. |
| format | Article |
| id | doaj-art-e4bf339c8ec14949aab81593d3da603e |
| institution | Kabale University |
| issn | 2215-0161 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | MethodsX |
| spelling | doaj-art-e4bf339c8ec14949aab81593d3da603e2025-01-21T04:13:08ZengElsevierMethodsX2215-01612025-06-0114103160On derived t-path, t=2,3 signed graph and t-distance signed graphDeepa Sinha0Sachin Somra1Corresponding author.; Department of Mathematics, Faculty of Mathematics and Computer Science, South Asian University, New Delhi 110068, IndiaDepartment of Mathematics, Faculty of Mathematics and Computer Science, South Asian University, New Delhi 110068, IndiaA signed graph Σ is a pair Σ=(Σu,σ)that consists of a graph (Σu,E) and a sign mapping called signature σ from E to the sign group {+,−}. In this paper, we discuss the t-path product signed graph (Σ)^twhere vertex set of (Σ)^t is the same as that of Σ and two vertices are adjacent if there is a path of length t, between them in the signed graph Σ. The sign of an edge in the t-path product signed graph is determined by the product of marks of the vertices in the signed graph Σ, where the mark of a vertex is the product of signs of all edges incident to it. In this paper, we provide a characterization of Σ which are switching equivalent to t-path product signed graphs (Σ)^t for t=2,3 which are switching equivalent to Σ and also the negation of the signed graph ŋ(Σ) that are switching equivalent to (Σ)^t for t=2,3. We also characterize signed graphs that are switching equivalent to t-distance signed graph (Σ¯)t for t=2 where 2-distance signed graph (Σ¯)2=(V′,E′,σ′) defined as follows: the vertex set is same as the original signed graph Σ and two vertices u,v∈(Σ¯)2, are adjacent if and only if there exists a distance of length two in Σ. The edge uv∈(Σ¯)2 is negative if and only if all the edges, in all the distances of length two in Σ are negative otherwise the edge is positive. The t-path network along with these characterizations can be used to develop model for the study of various real life problems communication networks. • t-path product signed graph. • t-distance signed graph.http://www.sciencedirect.com/science/article/pii/S2215016125000081t-path product and t-distance signed graph |
| spellingShingle | Deepa Sinha Sachin Somra On derived t-path, t=2,3 signed graph and t-distance signed graph MethodsX t-path product and t-distance signed graph |
| title | On derived t-path, t=2,3 signed graph and t-distance signed graph |
| title_full | On derived t-path, t=2,3 signed graph and t-distance signed graph |
| title_fullStr | On derived t-path, t=2,3 signed graph and t-distance signed graph |
| title_full_unstemmed | On derived t-path, t=2,3 signed graph and t-distance signed graph |
| title_short | On derived t-path, t=2,3 signed graph and t-distance signed graph |
| title_sort | on derived t path t 2 3 signed graph and t distance signed graph |
| topic | t-path product and t-distance signed graph |
| url | http://www.sciencedirect.com/science/article/pii/S2215016125000081 |
| work_keys_str_mv | AT deepasinha onderivedtpatht23signedgraphandtdistancesignedgraph AT sachinsomra onderivedtpatht23signedgraphandtdistancesignedgraph |