# The Roller-Coaster Conjecture Revisited

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- Further Properties of Trees with Minimal Atom-Bond Connectivity Index. Jianping Liu; Jinsong Chen // Abstract & Applied Analysis;2014, p1
Let G = (V, E) be a graph the atom-bond connectivity (ABC) index is defined as the sum of weights ((du + dv - 2 ) /dudv)1/2 over all edges uv of G, where du denotes the degree of a vertex u of G. In this paper, we determined a few structural features of the trees with minimal ABC index also we...

- Some Properties on Estrada Index of Folded Hypercubes Networks. Jia-Bao Liu; Xiang-Feng Pan; Jinde Cao // Abstract & Applied Analysis;2014, p1
Let G be a simple graph with n vertices and let Î»1, Î»2,...,Î»n be the eigenvalues of its adjacency matrix; the Estrada index EE(G) of the graph G is defined as the sum of the terms eÎ»i, i = 1,2,...,n. The n-dimensional folded hypercube networks FQn are an important and attractive...

- Vertex Equitable Labeling of Cycle and Star Related Graphs. Jeyanthi, P.; Maheswari, A.; Vijayalaksmi, M. // Journal of Scientific Research;2015, Vol. 7 Issue 3, p33
Let G be a graph with p vertices and q edges and A = 0,1,2,..., A vertex labeling f: V (G) -> A induces an edge labeling f* defined by f*(uv) = f(u) + f(v) for all edges uv. For aâˆˆ A, let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there...

- On (k,kn-k2-2k-1)-Choosability of n-Vertex Graphs. Charoenpanitseri, Wongsakorn // International Journal of Mathematics & Mathematical Sciences;5/12/2015, Vol. 2015, p1
A (k,t)-list assignment L of a graph G is a mapping which assigns a set of size k to each vertex v of G and |â‹ƒvâˆˆV(G)â€L(v)|=t. A graph G is (k,t)-choosable if G has a proper coloring f such that f(v)âˆˆL(v) for each (k,t)-list assignment L. In 2011, Charoenpanitseri et al....

- Some Results on Vertex Version and Edge Versions of Modified Schultz Index. Azari, Mahdieh // International Journal of Mathematical Combinatorics;2016, Vol. 2, p65
Let G1 and G2 be two simple connected graphs with disjoint vertex sets V(G1) and V(G2), respectively. For given vertices a1 G V(G1) and a2 âˆˆ V(G2), a splice of âˆˆ1 and G2 by vertices a1 and a2 is defined by identifying the vertices a1 and a2 in the union of G1 and G2 and a link of G1...

- A note on the augmented Zagreb index of cacti with fixed number of vertices and cycles. Ali, Akbar; Bhatti, Akhlaq A. // Kuwait Journal of Science;2016, Vol. 43 Issue 4, p11
Recent studies show that augmented Zagreb index ( AZI ) possess the best correlating ability among various well known topological indices for predicting the certain physicochemical properties of particular types of molecules. Hence, it is meaningful to study the mathematical properties of AZI...

- On 3-Regular Bipancyclic Subgraphs of Hypercubes. Borse, Y. M.; Shaikh, S. R. // International Journal of Combinatorics;5/5/2015, Vol. 2015, p1
The n-dimensional hypercube Qn is bipancyclic; that is, it contains a cycle of every even length from 4 to 2n. In this paper, we prove that Qnâ€‰â€‰(nâ‰¥3) contains a 3-regular, 3-connected, bipancyclic subgraph with l vertices for every even l from 8 to 2n except 10.

- The Minimum Equitable Domination Energy of a Graph. Rajendra, P.; Rangarajan, R. // International Journal of Mathematical Combinatorics;Sep2015, Vol. 3, p62
A subset D of V is called an equitable dominating set [8] if for every v âˆˆ V -D there exists a vertex u âˆˆ D such that uv âˆˆ E(G) and |deg(u) - deg(v)| â‰¤ 1, where deg(u) denotes the degree of vertex u and deg(v) denotes the degree of vertex v. Recently, The minimum covering...

- Reduction Theorem for Lattice Cohomology. László, Tamás; Némethi, András // IMRN: International Mathematics Research Notices;2015, Vol. 2015 Issue 11, p2938
The lattice cohomology of a plumbed 3-manifold M associated with a connected negative definite plumbing graph is an important tool in the study of topological properties of M and in the comparison of the topological properties with analytic ones, whenever M is realized as complex analytic...

- Semientire Equitable Dominating Graphs. Basavanagoud, B.; Kulli, V. R.; Teli, Vijay V. // International Journal of Mathematical Combinatorics;Sep2014, Vol. 3, p49
The semientire equitable dominating graph SEqD(G) of a graph G = (V, E) is the graph with vertex set Vâ‹ƒS, where S is the collection of all minimal equitable dominating sets of G and with two vertices u, v G Vâ‹ƒS adjacent if u, vâˆŠD, where D is the minimal equitable dominating set...