Results 21 to 30 of about 175,962 (155)
On the maximum ABC index of bipartite graphs without pendent vertices
Open Chemistry, 2020 For a simple graph G, the atom–bond connectivity index (ABC) of G is defined as ABC(G) = ∑ u v ∈ E ( G ) d ( u ) + d ( v ) − 2 d ( u ) d ( v ) , $\sum_{uv\in{}E(G)} \sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}},$where d(v) denotes the degree of vertex v of G.
Z. Shao +4 more
semanticscholar +1 more source
Bounds for the Kirchhoff Index of Bipartite Graphs
Journal of Applied Mathematics, 2012 A -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell consists of the path together with a independent vertices adjacent to one pendent vertex of and b independent ...
Yujun Yang
doaj +1 more source
Two classes of non-Leech trees
Electronic Journal of Graph Theory and Applications, 2020 Let T be a tree of order n. For any edge labeling f : E → {1,2,3,...} the weight of a path P is the sum of the labels of the edges of P and is denoted by w(P).
Seena Varghese +2 more
doaj +1 more source
The Connectivity and the Harary Index of a Graph [PDF]
, 2012 The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paper we provide an upper bound of the Harary index in terms of the vertex or edge connectivity of a graph.
Das +17 more
core +1 more source
On the Maximum ABC Index of Graphs With Prescribed Size and Without Pendent Vertices
IEEE Access, 2018 The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants, which are found in a vast variety of chemical applications. For a simple graph $G$ , it is defined as $ABC(G)=\sum _{uv \in E(G)} ({({d(u)+d(v)-2})
Z. Shao +4 more
semanticscholar +1 more source
On the Trees With Maximal Augmented Zagreb Index
IEEE Access, 2018 The augmented Zagreb index (AZI), a variant of the well-known atom-bond connectivity (ABC) index, was shown to have the best predicting ability for a variety of physicochemical properties among several tested vertex-degree-based topological indices ...
Wenshui Lin +4 more
doaj +1 more source
, 2017 The zeroth-order general Randi\'c index (usually denoted by $R_{\alpha}^{0}$) and variable sum exdeg index (denoted by $SEI_{a}$) of a graph $G$ are defined as $R_{\alpha}^{0}(G)= \sum_{v\in V(G)} (d_{v})^{\alpha}$ and $SEI_{a}(G)= \sum_{v\in V(G)}d_{v}a^
Ali, Akbar, Khalid, Sohaib
core +1 more source
, 2020 A graceful labeling of a graph $G$ with $m$ edges consists of labeling the vertices of $G$ with distinct integers from $0$ to $m$ such that, when each edge is assigned as induced label the absolute difference of the labels of its endpoints, all induced ...
Dantas, Simone +2 more
core +2 more sources
On maximum signless Laplacian Estrada index of graphs with given parameters II
Electronic Journal of Graph Theory and Applications, 2018 The signless Laplacian Estrada index of a graph G is defined as SLEE(G) = ∑ni = 1eqi where q1, q2, …, qn are the eigenvalues of the signless Laplacian matrix of G.
Ramin Nasiri +3 more
doaj +1 more source
, 2012 The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3.
A. Bjorklund +9 more
core +1 more source