TY - JOUR AU - Sehgal, Amit AU - Manjeet, AU - Singh, Dalip PY - 2021 TI - Co-prime order graphs of finite Abelian groups and dihedral groups JO - Journal of Mathematics and Computer Science SP - 196--202 VL - 23 IS - 3 AB - The co-prime order graph \(\Theta (G)\) of a given finite group is a simple undirected graph whose vertex set is the group \(G\) itself, and any two vertexes \(x,y\) in \(\Theta (G)\) are adjacent if and only if \(gcd(o(x),o(y))=1\) or prime. In this paper, we derive a precise formula to count the vertex's degree in the co-prime order graph of a finite Abelian group or dihedral group.We also investigate the Laplacian spectrum of the co-prime order graph \(\Theta (G)\) when G is a finite Abelian p-group, \({\mathbb{Z}_p}^t \times {\mathbb{Z}_q}^s\) or a dihedral group \(D_{p^n}\). SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.023.03.03 DO - 10.22436/jmcs.023.03.03 ID - Sehgal2021 ER - TY - JOUR TI - Power graphs: a survey AU - J. Abawajy AU - A. Kelarev AU - M. Chowdhury JO - Electron. J. Graph Theory Appl. (EJGTA) PY - 2013 DA - 2013// VL - 1 ID - Abawajy2013 ER - TY - JOUR TI - On a New Graph defined on the order of elements of a Finite Group AU - S. Banerjee JO - arXiv PY - 2019 DA - 2019// VL - 2019 ID - Banerjee2019 ER - TY - JOUR TI - Cayley graphs for some well-known groups AU - F. Budden JO - Math. Gaz. PY - 1985 DA - 1985// VL - 69 ID - Budden1985 ER - TY - JOUR TI - Undirected power graphs of semigroups AU - I. Chakrabarty AU - S. Ghosh AU - M. K. Sen JO - Semigroup Forum PY - 2009 DA - 2009// VL - 78 ID - Chakrabarty2009 ER - TY - JOUR TI - A fixed point theorem for asymptotically nonexpansive mappings AU - K. Goebel AU - W. A. Kirk JO - Proc. Amer. Math. Soc. PY - 1972 DA - 1972// VL - 35 ID - Goebel1972 ER - TY - BOOK TI - Matrix analysis AU - R. A. Horn AU - C. R. Johnson PB - Cambridge University Press PY - 2013 DA - 2013// CY - Cambridge ID - Horn2013 ER - TY - JOUR TI - A Combinatorial property and power graphs of Groups AU - A. V. Kelarev AU - S. J. Quinn JO - Contributions to general algebra PY - 1999 DA - 1999// VL - 12 ID - Kelarev1999 ER - TY - JOUR TI - The coprime graph of a group AU - X. Ma AU - H. Wei AU - L. Yang JO - Int. J. Group Theory PY - 2014 DA - 2014// VL - 3 ID - Ma2014 ER - TY - JOUR TI - On the minimum degree, edge-connectivity and connectivity of power graphs of finite groups AU - R. P. Panda AU - K. V. Krishna JO - Comm. Algebra PY - 2018 DA - 2018// VL - 46 ID - Panda2018 ER - TY - JOUR TI - On the minimum degree of the power graph of a finite cyclic group AU - R. P. Panda AU - K. L. Patra AU - B. K. Sahoo JO - J. Algebra Appl. PY - 2020 DA - 2020// VL - 2020 ID - Panda2020 ER - TY - JOUR TI - The degree of a vertex in the power graph of a finite abelian group AU - A. Sehgal AU - S. N. Singh JO - arXiv PY - 2019 DA - 2019// VL - 2019 ID - Sehgal2019 ER -