scholarly journals The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1277
Author(s):  
Michal Staš
Keyword(s):  
Connected Graph ◽  
Crossing Numbers ◽  
Tripartite Graph ◽  
Complete Tripartite Graph

The main aim of the paper is to establish the crossing numbers of the join products of the paths and the cycles on n vertices with a connected graph on five vertices isomorphic to the graph K1,1,3\e obtained by removing one edge e incident with some vertex of order two from the complete tripartite graph K1,1,3. The proofs are done with the help of well-known exact values for the crossing numbers of the join products of subgraphs of the considered graph with paths and cycles. Finally, by adding some edges to the graph under consideration, we obtain the crossing numbers of the join products of other graphs with the paths and the cycles on n vertices.

On the line graph of the complete tripartite graph

1977 ◽  
Vol 5 (1) ◽  
pp. 19-25 ◽  
Author(s):  
A.J. Hoffman ◽  
Basharat A. Jamil
Keyword(s):  
Line Graph ◽  
Tripartite Graph ◽  
Complete Tripartite Graph

scholarly journals Power of 2 Decomposition of a Complete Tripartite Graph K2,4,M and a Special Butterfly Graph

2020 ◽  
Vol 9 (3) ◽  
pp. 3973-3976
Keyword(s):  
Simple Graph ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Edge Disjoint ◽  
Tripartite Graph ◽  
Necessary And Sufficient ◽  
Complete Tripartite Graph

Let G be a finite, connected simple graph with p vertices and q edges. If G1 , G2 ,…, Gn are connected edge-disjoint subgraphs of G with E(G) = E(G1 )  E(G2 )  …  E(Gn) , then {G1 , G2 , …, Gn} is said to be a decomposition of G. A graph G is said to have Power of 2 Decomposition if G can be decomposed into edge-disjoint subgraphs G G G n  2 4 2 , ,..., such that each G i 2 is connected and ( ) 2 , i E Gi  for 1  i  n. Clearly, 2[2 1] n q . In this paper, we investigate the necessary and sufficient condition for a complete tripartite graph K2,4,m and a Special Butterfly graph           3 2 5 BF 2m 1 to accept Power of 2 Decomposition.

scholarly journals Asymptotically optimal induced decompositions

2014 ◽  
Vol 8 (2) ◽  
pp. 320-329
Author(s):  
Veronika Halász ◽  
Zsolt Tuza
Keyword(s):  
Graph Theory ◽  
Lower Bound ◽  
Complete Multipartite Graph ◽  
Asymptotically Optimal ◽  
Asymptotic Growth ◽  
Tripartite Graph ◽  
Multipartite Graph ◽  
Complete Multipartite ◽  
Complete Tripartite Graph

Solving a problem raised by Bondy and Szwarcfiter [J. Graph Theory, 72 (2013), 462-477] we prove that if the edge set of a graph G of order n can be decomposed into edge-disjoint induced copies of the path P4 or of the paw K4?P3, then the complement of G has at least cn3/2 edges. This lower bound is tight apart from the actual value of c, and completes the determination of asymptotic growth for the graphs with at most four vertices. More generally the lower bound cn3/2 holds for any graph without isolated vertices which is not a complete multipartite graph; but a linear upper bound is valid for any complete tripartite graph.

scholarly journals Saturation Number of $tK_{l,l,l}$ in the Complete Tripartite Graph

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Zhen He ◽  
Mei Lu
Keyword(s):  
Tripartite Graph ◽  
Minimum Number ◽  
Saturation Number ◽  
Complete Tripartite Graph

For  fixed graphs $F$ and $H$, a graph $G\subseteq F$ is $H$-saturated if there is no copy of $H$ in $G$, but for any edge $e\in E(F)\setminus E(G)$, there is a copy of $H$ in $G+e$. The saturation number of $H$ in $F$, denoted $sat(F,H)$, is the minimum number of edges in an $H$-saturated subgraph of $F$.  In this paper, we study saturation numbers of $tK_{l,l,l}$ in complete tripartite graph $K_{n_1,n_2,n_3}$. For $t\ge 1$, $l\ge 1$ and $n_1,n_2$ and $n_3$ sufficiently large, we determine  $sat(K_{n_1,n_2,n_3},tK_{l,l,l})$ exactly.

Sign in / Sign up

Export Citation Format

Share Document