Total domination dot-critical graphs

Michael A. Henning; Nader Jafari Rad

doi:10.1016/j.dam.2010.10.006

Total domination dot-critical graphs

Michael A. Henning
, Nader Jafari Rad

Mathematics and Applied Mathematics

Shahrood University of Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

A graph G with no isolated vertex is total domination vertex-critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G-v is less than the total domination number of G. A graph is total domination dot-critical if contracting any edge decreases the total domination number. In this paper, we study total domination dot-critical graphs. We present several properties of these graphs. We show that the total domination dot-critical graphs include the total domination vertex-critical graphs.

Original language	English
Pages (from-to)	104-111
Number of pages	8
Journal	Discrete Applied Mathematics
Volume	159
Issue number	2-3
DOIs	https://doi.org/10.1016/j.dam.2010.10.006
Publication status	Published - 2011

Keywords

Critical
Dot-critical
Total domination

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2010.10.006

Cite this

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title = "Total domination dot-critical graphs",

abstract = "A graph G with no isolated vertex is total domination vertex-critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G-v is less than the total domination number of G. A graph is total domination dot-critical if contracting any edge decreases the total domination number. In this paper, we study total domination dot-critical graphs. We present several properties of these graphs. We show that the total domination dot-critical graphs include the total domination vertex-critical graphs.",

keywords = "Critical, Dot-critical, Total domination",

author = "Henning, \{Michael A.\} and Rad, \{Nader Jafari\}",

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journal = "Discrete Applied Mathematics",

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AU - Henning, Michael A.

AU - Rad, Nader Jafari

PY - 2011

Y1 - 2011

N2 - A graph G with no isolated vertex is total domination vertex-critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G-v is less than the total domination number of G. A graph is total domination dot-critical if contracting any edge decreases the total domination number. In this paper, we study total domination dot-critical graphs. We present several properties of these graphs. We show that the total domination dot-critical graphs include the total domination vertex-critical graphs.

AB - A graph G with no isolated vertex is total domination vertex-critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G-v is less than the total domination number of G. A graph is total domination dot-critical if contracting any edge decreases the total domination number. In this paper, we study total domination dot-critical graphs. We present several properties of these graphs. We show that the total domination dot-critical graphs include the total domination vertex-critical graphs.

KW - Critical

KW - Dot-critical

KW - Total domination

UR - https://www.scopus.com/pages/publications/78649634974

U2 - 10.1016/j.dam.2010.10.006

DO - 10.1016/j.dam.2010.10.006

M3 - Article

AN - SCOPUS:78649634974

SN - 0166-218X

VL - 159

SP - 104

EP - 111

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 2-3

ER -

Total domination dot-critical graphs

Abstract

Keywords

ASJC Scopus subject areas

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