DISTANCE SPECTRUM OF TWO FAMILIES OF GRAPHS
- Title
- DISTANCE SPECTRUM OF TWO FAMILIES OF GRAPHS
- Creator
- Thomas A.S.; Kalayathankal S.J.; Kureethara J.V.
- Description
- Let H1 and H2 be two copies of the complete graph Kn, n ? 3 with vertex sets V(H1) = {v1,v2...,vn} and V(H2) = {u1,u2,...,un}. Graph ?(n,p), 1 ? p ? n-1, is obtained from the union of graphs H1 and H2 by adding edges {uivi)|i ? {1, 2...,p}}. Graph ?(n) is obtained from the union of graphs H1 and H2 by joining each vertex vi of H1 to every vertex in {u1, u2, ..., un} \ {ui}, i = 1, 2, ..., n. The adjacency spectrum of ?(n, p) and ?(n) were determined in [9]. An open problem posed in [7] was to find families of graphs of diameter greater than two, for which the adjacency and distance spectrum are both integral. To answer the open problem, the distance spectrum of the above family of graphs is calculated, and new distance equienergetic graphs are constructed in this paper. 2024 Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved.
- Source
- Proceedings of the Jangjeon Mathematical Society, Vol-27, No. 4, pp. 849-857.
- Date
- 2024-01-01
- Publisher
- Jangjeon Research Institute for Mathematical Sciences and Physics
- Subject
- distance spectrum; equienergetic graphs; integral graphs
- Coverage
- Thomas A.S., Department of Mathematics, Catholicate College, Kerala, Pathanamthitta, 689645, India, Department of Mathematics, St Thomas College, Kerala, Kozhencherry, 689641, India; Kalayathankal S.J., Department of Mathematics, Catholicate College, Kerala, Pathanamthitta, 689645, India, Jyothi Engineering College, Cheruthuruthy, Kerala, Thrissur, 679531, India; Kureethara J.V., Department of Mathematics, Christ University, Bangalore, 560029, India
- Rights
- Restricted Access
- Relation
- ISSN: 15987264
- Format
- Online
- Language
- English
- Type
- Article
Collection
Citation
Thomas A.S.; Kalayathankal S.J.; Kureethara J.V., “DISTANCE SPECTRUM OF TWO FAMILIES OF GRAPHS,” CHRIST (Deemed To Be University) Institutional Repository, accessed February 24, 2025, https://archives.christuniversity.in/items/show/13433.