# b-CHROMATIC NUMBER OF T(K1, n, n ), T(F1, n ), T(Bn, n ), T(Km, n ), T(Cn ) AND T(Pn )

## Related Articles

- Influence of the tie-break rule on the end-vertex problem. Charbit, Pierre; Habib, Michel; Mamcarz, Antoine // Discrete Mathematics & Theoretical Computer Science (DMTCS);2014, Vol. 16 Issue 2, p57
End-vertices of a given graph search may have some nice properties, as for example it is well known that the last vertex of Lexicographic Breadth First Search (LBFS) in a chordal graph is simplicial, see Rose, Tarjan and Lueker 1976. Therefore it is interesting to consider if these vertices can...

- The second largest value of the sum of squares of degrees in bipartite graphs with few edges. Zhou Chun-cao; Chen Bo-lin // Basic Sciences Journal of Textile Universities / Fangzhi Gaoxia;Mar2010, Vol. 23 Issue 1, p7
The second largest value of the sum of squares of degrees with a given number of vertices and few edges for bipartite graphs is studyed. After determining the bipartite graphs with few edges where the sum of the squares of degrees is maximum, the second largest value is determined by comparing...

- P6- and Triangle-Free Graphs Revisited: Structure and Bounded Clique-Width. Brandst�dt, Andreas; Klembt, Tilo; Mahfud, Suhail // Discrete Mathematics & Theoretical Computer Science (DMTCS);Jun2005, Vol. 8 Issue 1, p173
The Maximum Weight Stable Set (MWS) Problem is one of the fundamental problems on graphs. It is well-known to be NP-complete for triangle-free graphs, and Mosca has shown that it is solvable in polynomial time when restricted to P6- and triangle-free graphs. We give a complete structure analysis...

- Vertex-Distinguishing E-Total Colorings of Graphs. Chen, Xiang'en; Zu, Yue; Xu, Jin; Wang, Zhiwen; Yao, Bing // Arabian Journal for Science & Engineering (Springer Science & Bu;Dec2011, Vol. 36 Issue 8, p1485
Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex u of G let C( u) or C( u) denote the set...

- Uniquely monopolar-partitionable block graphs. Xuegang Chen; Jing Huang // Discrete Mathematics & Theoretical Computer Science (DMTCS);2014, Vol. 16 Issue 2, p21
As a common generalization of bipartite and split graphs, monopolar graphs are defined in terms of the existence of certain vertex partitions. It has been shown that to determine whether a graph has such a partition is an NPcomplete problem for general graphs, and is polynomial time solvable for...

- On Extremal Unicyclic Molecular Graphs with Prescribed Girth and Minimal Hosoya Index. Jianping Ou // Journal of Mathematical Chemistry;Oct2007, Vol. 42 Issue 3, p423
Let G be an n-vertex unicyclic molecular graph and Z(G) be its Hosoya index, let F n be the nth Fibonacci number. It is proved in this paper that if G has girth l then Z(G) â‰¥ F l+1+(nâˆ’l)F l +F l-1, with the equality holding if and only if G is isomorphic to $$S_n^l$$, the...

- A NEW GRAPH DRAWING ALGORITHM THAT CONSIDERS A FOCUS VERTEX. Abe, Noboru; Sakai, Goh // Advances in Computer Science & Engineering;May2013, Vol. 10 Issue 2, p107
Let G be a connected undirected graph, and let R be the minimum axis-parallel rectangle that includes all the vertices of a drawing of G. Herein, we consider the problem of drawing G containing one particularly important notable vertex. It is desirable that this notable vertex, which we call the...

- Game-perfect graphs. Andres, Stephan Dominique // Mathematical Methods of Operations Research;2009, Vol. 69 Issue 2, p235
A graph coloring game introduced by Bodlaender (Int J Found Comput Sci 2:133â€“147, 1991) as coloring construction game is the following. Two players, Alice and Bob, alternately color vertices of a given graph G with a color from a given color set C, so that adjacent vertices receive...

- Partial characterizations of coordinated graphs: line graphs and complements of forests. Bonomo, Flavia; Durán, Guillermo; Soulignac, Francisco; Sueiro, Gabriel // Mathematical Methods of Operations Research;2009, Vol. 69 Issue 2, p251
A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color is equal to the maximum number of cliques of H with a common vertex, for every induced subgraph H of G....