Intersection graph of gamma sets in the total graph

T. Tamizh Chelvam; T. Asir

Discussiones Mathematicae Graph Theory (2012)

  • Volume: 32, Issue: 2, page 341-356
  • ISSN: 2083-5892

Abstract

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In this paper, we consider the intersection graph I Γ ( ℤ ₙ ) of gamma sets in the total graph on ℤₙ. We characterize the values of n for which I Γ ( ℤ ₙ ) is complete, bipartite, cycle, chordal and planar. Further, we prove that I Γ ( ℤ ₙ ) is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivity and some domination parameters of I Γ ( ℤ ₙ ) .

How to cite

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T. Tamizh Chelvam, and T. Asir. "Intersection graph of gamma sets in the total graph." Discussiones Mathematicae Graph Theory 32.2 (2012): 341-356. <http://eudml.org/doc/270932>.

@article{T2012,
abstract = {In this paper, we consider the intersection graph $I_\{Γ\}(ℤₙ)$ of gamma sets in the total graph on ℤₙ. We characterize the values of n for which $I_\{Γ\}(ℤₙ)$ is complete, bipartite, cycle, chordal and planar. Further, we prove that $I_\{Γ\}(ℤₙ)$ is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivity and some domination parameters of $I_\{Γ\}(ℤₙ)$.},
author = {T. Tamizh Chelvam, T. Asir},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {total graph; gamma sets; intersection graph; Hamiltonian; coloring; connectivity; domination number; independence number; clique number},
language = {eng},
number = {2},
pages = {341-356},
title = {Intersection graph of gamma sets in the total graph},
url = {http://eudml.org/doc/270932},
volume = {32},
year = {2012},
}

TY - JOUR
AU - T. Tamizh Chelvam
AU - T. Asir
TI - Intersection graph of gamma sets in the total graph
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 2
SP - 341
EP - 356
AB - In this paper, we consider the intersection graph $I_{Γ}(ℤₙ)$ of gamma sets in the total graph on ℤₙ. We characterize the values of n for which $I_{Γ}(ℤₙ)$ is complete, bipartite, cycle, chordal and planar. Further, we prove that $I_{Γ}(ℤₙ)$ is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivity and some domination parameters of $I_{Γ}(ℤₙ)$.
LA - eng
KW - total graph; gamma sets; intersection graph; Hamiltonian; coloring; connectivity; domination number; independence number; clique number
UR - http://eudml.org/doc/270932
ER -

References

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