A Study on Signed Domatic Number of a Graph

@article{1703741,
      author = {M. S. Patil},
      title = {A Study on Signed Domatic Number of a Graph},
      journal = {Iconic Research And Engineering Journals},
      year = {2022},
      volume = {6},
      number = {2},
      pages = {279-288},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1703741.pdf},
      abstract = {A two-valued function f defined on the vertices of a graph G = (V, E),	f: V -> {?1, 1} is a Signed dominating function, if the sum of its function values over any closed neighborhood is at least one. The weight of a signed dominating function is w (f ) = E f (v), over all vertices v ? V. The signed domination number of a graph G, is denoted by Ys(G), equals the minimum weight of a signed dominating function of G. A set f1, f2, f3, ...., fd of signed dominating functions on G with the property that E fi(x) <= 1 for each x E V (G), is called a signed dominating function i=1 on G. The maximum number of functions in a signed dominating family on G is the signed domatic number of G, denoted by ds(G). In this paper, we prove Ys(G) + ds(G) <= n + 1 and ds(G) + ds(G?) <= n + 1. Further, we characterize the class of extremal class of graphs for which both the bounds attain. And to find the exact value of signed domatic number of a circulant graphs. Throughout this paper, we consider only finite, undirected simple graphs we mean without multiple edges or loops.},
      keywords = {Signed dominating function, Signed domination number, Signed domatic number, AMS Classification:05C},
      month = {August},
  }