scholarly journals A Rao-type characterization for a sequence to have a realization containing a split graph

2011 ◽  
Vol 311 (21) ◽  
pp. 2485-2489 ◽  
Author(s):  
Jian-Hua Yin
Keyword(s):  
Split Graph

Split Graphs with Specified Dilworth Numbers

1984 ◽  
Vol 27 (1) ◽  
pp. 43-47
Author(s):  
Chiê Nara ◽  
Iwao Sato
Keyword(s):  
Induced Subgraph ◽  
Split Graph ◽  
Complete Part ◽  
Split Graphs

AbstractLet G be a split graph with the independent part IG and the complete part KG. Suppose that the Dilworth number of (IG, ≼) with respect to the vicinal preorder ≼ is two and that of (KG, ≼) is an integer k. We show that G has a specified graph Hk, defined in this paper, as an induced subgraph.

Clique Partitions of Chordal Graphs

1993 ◽  
Vol 2 (4) ◽  
pp. 409-415 ◽  
Author(s):  
Paul Erdős ◽  
Edward T. Ordman ◽  
Yechezkel Zalcstein
Keyword(s):  
Chordal Graph ◽  
Chordal Graphs ◽  
Split Graph ◽  
Threshold Graph

To partition the edges of a chordal graph on n vertices into cliques may require as many as n2/6 cliques; there is an example requiring this many, which is also a threshold graph and a split graph. It is unknown whether this many cliques will always suffice. We are able to show that (1 − c)n2/4 cliques will suffice for some c > 0.

scholarly journals Determining Numbers of Coloring λ-Backbone On Split Graph

2020 ◽  
Vol 1569 ◽  
pp. 042074
Author(s):  
Fatanur Baity Tsulutsya ◽  
Evawati Alisah ◽  
Lailiy Kurnia Ilahi
Keyword(s):  
Split Graph

scholarly journals Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Xiaolin Chen ◽  
Huishu Lian
Keyword(s):  
Split Graph ◽  
Matching Polynomial ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
The Absolute ◽  
Complete Multipartite ◽  
The Given ◽  
Turán Graph

The matching energy ME(G) of a graph G was introduced by Gutman and Wagner, which is defined as the sum of the absolute values of the roots of the matching polynomial m(G,x). The largest matching root λ1(G) is the largest root of the matching polynomial m(G,x). Let Kn1,n2,…,nr denote the complete r-partite graph with order n=n1+n2+…+nr, where r>1. In this paper, we prove that, for the given values n and r, both the matching energy ME(G) and the largest matching root λ1(G) of complete r-partite graphs are minimal for complete split graph CS(n,r-1) and are maximal for Turán graph T(n,r).

Structure of super strongly perfect graphs

2021 ◽  
Author(s):  
T. E. Soorya ◽  
Sunil Mathew
Keyword(s):  
Line Graph ◽  
Perfect Graphs ◽  
Split Graph ◽  
Counter Example ◽  
Existing Result

Super strongly perfect graphs and their association with certain other classes of graphs are discussed in this paper. It is observed that every split graph is super strongly perfect. An existing result on super strongly perfect graphs is disproved providing a counter example. It is also established that if a graph [Formula: see text] contains a cycle of odd length, then its line graph [Formula: see text] is not always super strongly perfect. Complements of cycles of length six or above are proved to be non-super strongly perfect. If a graph is strongly perfect, then it is shown that they are super strongly perfect and hence all [Formula: see text]-free graphs are super strongly perfect.

scholarly journals On the local adjacency metric dimension of split graph

2019 ◽  
Vol 243 ◽  
pp. 012076
Author(s):  
E R Albirri ◽  
Dafik ◽  
I H Agustin ◽  
R Alfarisi ◽  
R M Prihandini ◽  
...  
Keyword(s):  
Metric Dimension ◽  
Split Graph

scholarly journals On the General Position Number of Complementary Prisms

2021 ◽  
Vol 178 (3) ◽  
pp. 267-281
Author(s):  
P. K. Neethu ◽  
S.V. Ullas Chandran ◽  
Manoj Changat ◽  
Sandi Klavžar
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
General Position ◽  
Disjoint Union ◽  
Perfect Matching ◽  
Split Graph ◽  
Block Graphs ◽  
Disconnected Graphs ◽  
Complementary Prism ◽  
Sharp Lower Bound

The general position number gp(G) of a graph G is the cardinality of a largest set of vertices S such that no element of S lies on a geodesic between two other elements of S. The complementary prism G G ¯ of G is the graph formed from the disjoint union of G and its complement G ¯ by adding the edges of a perfect matching between them. It is proved that gp(G G ¯ ) ≤ n(G) + 1 if G is connected and gp(G G ¯ ) ≤ n(G) if G is disconnected. Graphs G for which gp(G G ¯ ) = n(G) + 1 holds, provided that both G and G ¯ are connected, are characterized. A sharp lower bound on gp(G G ¯ ) is proved. If G is a connected bipartite graph or a split graph then gp(G G ¯ ) ∈ {n(G), n(G)+1}. Connected bipartite graphs and block graphs for which gp(G G ¯ ) = n(G) + 1 holds are characterized. A family of block graphs is constructed in which the gp-number of their complementary prisms is arbitrary smaller than their order.

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