Connected Total Monophonic Eccentric Domination in Graphs

EasyChair Preprint no. 3024

Abstract

For any two vertices x and y in a non-trivial connected graph G, the monophonic distance d_m(x,y) is the length of a longest monophonic path joining the vertices x and y in G. The monophonic eccentricity of a vertex x is defined as e_m(x) = max {d_m(x,y): y ∈ V(G)}. A vertex y in G is a monophonic eccentric vertex of a vertex x in G if e_m(x) = d_m(x,y). A set S ⊆ V in a graph G is a total monophonic eccentric dominating set if every vertex of G has a monophonic eccentric vertex in S. The total monophonic eccentric  domination number ⋎_tme(G) is the  cardinality of a minimum total monophonic eccentric  dominating set of G. A set S ⊆ V in a graph G is a connected total monophonic eccentric  dominating set if S is a total monophonic eccentric dominating set and the induced subgraph ≺S≻ is connected. The connected total monophonic eccentric  domination number ⋎_ctme(G) is the  cardinality of a minimum connected total monophonic eccentric dominating set of G. We investigate some properties of connected total monophonic eccentric  dominating sets. Also, we determine the bounds of connected total monophonic eccentric domination number and find the same for some standard graphs.

Keyphrases: connected total monophonic eccentric dominating set, connected total monophonic eccentric domination number, monophonic eccentric vertex, total monophonic eccentric dominating set, total monophonic eccentric domination number

@Booklet{EasyChair:3024,
  author = {P. Titus and J. Ajitha Fancy},
  title = {Connected Total Monophonic Eccentric Domination in Graphs},
  howpublished = {EasyChair Preprint no. 3024},

  year = {EasyChair, 2020}}