g-Central Graph of a Group

摘要

For any group G and fixed element ? G, we associate a graph namely g-central graph of G whose vertices are all elements of G and two distinct vertices x and y are adjacent if and only if xgy ? Z(G) or ygx ? Z(G), where Z(G) is the center of G. In this paper, we determine connectivity, diameter, girth and some numerical invariants of the graph, for instance chromatic, dominating and independence numbers. Moreover, we state that when the graph is planar or Eulerian.