Open AccessSome relations between power graphs and Cayley graphs
Author(s) -
Sriparna Chattopadhyay,
Pratima Panigrahi
Publication year - 2015
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2015.01.004
Subject(s) - cayley graph , mathematics , combinatorics , indifference graph , chordal graph , pathwidth , maximal independent set , vertex (graph theory) , graph product , discrete mathematics , cograph , unitary state , 1 planar graph , graph , line graph , political science , law
Motivated by an open problem of Abawajy et al. [1] we find some relations between power graphs and Cayley graphs of finite cyclic groups. We show that the vertex deleted subgraphs of some power graphs are spanning subgraphs or equal to the complement of vertex deleted subgraphs of some unitary Cayley graphs. Also we prove that some Cayley graphs can be expressed as direct product of power graphs. Applying these relations we study the eigenvalues and energy of power graphs and the related Cayley graphs