Author/Authors :
Ramane, Harishchandra S Department of Mathematics - Karnatak University, Dahrwad- 580003, India , Gudodagi, Gouramma A Department of Mathematics - KLE Societys - Basavaprabhu Kore Arts - Science and Commerce College, Karnataka, India , Manjalapur, Vinayak V. Department of Mathematics - KLE Societys - Basavaprabhu Kore Arts - Science and Commerce College, Karnataka, India , Alhevaz, Abdollah Faculty of Mathematical Sciences - Shahrood University of Technology, Shahrood, Iran
Abstract :
Let D be the diameter and dG(vi, vj ) be the distance between
the vertices vi and vj of a connected graph G. The complementary
distance matrix of a graph G is CD(G) = [cdij ] in which cdij = 1 +D −
dG(vi, vj ) if i ≠ j and cdij = 0 if i = j. The complementary transmission
CTG(v) of a vertex v is defined as CTG(v) = Σu∈V (G)[1+D−dG(u, v)].
Let CT(G) = diag[CTG(v1),CTG(v2), . . . ,CTG(vn)]. The complementary
distance signless Laplacian matrix of G is CDL+(G) = CT(G) +
CD(G). In this paper, we obtain the bounds for the largest eigenvalue of
CDL+(G). Further we determine Nordhaus-Gaddum type results for the
largest eigenvalue. We also establish some bounds for the complementary
distance signless Laplacian energy.
Keywords :
complementary transmission regular graph , diameter , Complementary distance signless Laplacian matrix (energy)
