TY - JOUR
T1 - Complete (2,2) Bipartite Graphs
AU - Hanif, S.
AU - Bhat, K. A.
AU - Sudhakara, G.
N1 - Funding Information:
Authors are grateful for the insightful comments offered by the anonymous peer reviewers of the manuscript. Their generosity and expertise have improved this study in innumerable ways. Authors would also want to express our gratitude to Manipal Academy of Higher Education for providing with administrative support and resources.
Publisher Copyright:
© 2022. All Rights Reserved.
PY - 2022
Y1 - 2022
N2 - A bipartite graph G can be treated as a (1, 1) bipartite graph in the sense that, no two vertices in the same part are at distance one from each other. A (2, 2) bipartite graph is an extension of the above concept in which no two vertices in the same part are at distance two from each other. In this article, analogous to complete (1, 1) bipartite graphs which have the maximum number of pairs of vertices having distance one between them, a complete (2, 2) bipartite graph is defined as follows. A complete (2, 2) bipartite graph is a graph which is (2, 2) bipartite and has the maximum number of pairs of vertices (u, v) such that d(u, v) = 2. Such graphs are characterized and their properties are studied. The expressions are derived for the determinant, the permanent and spectral properties of some classes of complete (2, 2) bipartite graphs. A class of graphs among complete (2, 2) bipartite graphs having golden ratio in their spectrum is obtained.
AB - A bipartite graph G can be treated as a (1, 1) bipartite graph in the sense that, no two vertices in the same part are at distance one from each other. A (2, 2) bipartite graph is an extension of the above concept in which no two vertices in the same part are at distance two from each other. In this article, analogous to complete (1, 1) bipartite graphs which have the maximum number of pairs of vertices having distance one between them, a complete (2, 2) bipartite graph is defined as follows. A complete (2, 2) bipartite graph is a graph which is (2, 2) bipartite and has the maximum number of pairs of vertices (u, v) such that d(u, v) = 2. Such graphs are characterized and their properties are studied. The expressions are derived for the determinant, the permanent and spectral properties of some classes of complete (2, 2) bipartite graphs. A class of graphs among complete (2, 2) bipartite graphs having golden ratio in their spectrum is obtained.
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U2 - 10.47836/MJMS.16.2.13
DO - 10.47836/MJMS.16.2.13
M3 - Article
AN - SCOPUS:85131398885
SN - 1823-8343
VL - 16
SP - 379
EP - 390
JO - Malaysian Journal of Mathematical Sciences
JF - Malaysian Journal of Mathematical Sciences
IS - 2
ER -