Integrity of quasi-total graphs
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
A communication network can be considered to be highly vulnerable to dis- ruption if the failure of few members can result in no member's being able to communicate with very many others. This idea suggests the concept of the integrity of a graph. The integrity I(G) of a graph G is defined as I(G) = minS⊂V(G){|S|+m(G-S)} where m(G-S)denotes the order of the largest component of G-S. In this paper, we obtain the integrity of quasi-total graph of some standard graph families and combinations of these graphs. Further, we establish some relations connecting the integrity of some graph families and integrity of their quasi-total graphs.
Abstract
A communication network can be considered to be highly vulnerable to dis- ruption if the failure of few members can result in no member's being able to communicate with very many others. This idea suggests the concept of the integrity of a graph. The integrity I(G) of a graph G is defined as I(G) = minS⊂V(G){|S|+m(G-S)} where m(G-S)denotes the order of the largest component of G-S. In this paper, we obtain the integrity of quasi-total graph of some standard graph families and combinations of these graphs. Further, we establish some relations connecting the integrity of some graph families and integrity of their quasi-total graphs.
참고문헌 (14)
- Bagga, K.S, "A survey of integrity", Discrete Appl. Math, 37, pp.13~28 (1992)
- Bagga, K.S, "The Integrity of the Prism (Preliminary Report)", Abstracts Amer. Math. Soc, 10, pp.12~ (1989)
- Barefoot, C.A, "Vulnerability in Graphs - A Comparative Survey", J. Combin. Math. Combin. Comp, 1, pp.13~22 (1987)
- Barefoot, C.A, "Integrity of Trees and Powers of Cycles", Congr. Numer, 58, pp.103~114 (1987)
- Basavanagoud, B, "Quasi-total graphs with crossing numbers", J. Discrete Math. Cryptography, 1, pp.133~142 (1998)
- Basavanagoud, B, "On the Wiener index of quasi-total graph and its complement", Int. J. Math. Combin, 1, pp.82~90 (2016)
- Bondy, J.A, "Graph Theory with Applications" (1976), Macmillan
- Goddard, W.D, "On the Integrity of Combinations of Graphs", J. Commbin. Math. Combin. Comp, 4, pp.3~18 (1988)
- Goddard, W, "Integrity in Graphs, Bounds and Basics", J. Combin. Math. Combin. Comp, 7, pp.139~151 (1990)
- Goddard, W, "On the Vulnerability of Graphs", 박사, pp.1989
- Harary, F, "Graph Theory" (1969), Addison-Wesley
- Kulli, V.R, "Traversability and planarity of quasi-total graphs", Bull. Cal. Math. Soc, 94(1), pp.1~6 (2002)
- Kulli, V.R, "College Graph Theory" (2012), Vishwa International Publications
- Sastry, D.V.S, "Graph equations for line graphs, total graphs, middle graphs and quasi-total graphs", Discrete Math, 48, pp.113~119 (1984)