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70
On the Randić Index of Unicyclic Graphs with Fixed Diameter
"... Abstract The Randić index R(G) of a graph G is the sum of the weights of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we give sharp lower bounds of Randić index of unicyclic graphs with n vertices and diameter d, which partly confirms a conjecture in [1] (MATCH ..."
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Abstract The Randić index R(G) of a graph G is the sum of the weights of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we give sharp lower bounds of Randić index of unicyclic graphs with n vertices and diameter d, which partly confirms a conjecture in [1] (MATCH
The harmonic index of unicyclic graphs with given matching number
 Kragujevac J. Math
"... Abstract. The harmonic index of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, we determine the graph with minimum harmonic index among all unicyclic graphs with a perfect ma ..."
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matching. Moreover, the graph with minimum harmonic index among all unicyclic graphs with a given matching number is also determined.
On MerrifieldSimmons index of unicyclic graphs
"... with given girth and prescribed pendent vertices ∗ ..."
On the Randić index of unicyclic conjugated molecules
 J. Math. Chem
"... The Randic ́ index R(G) of a graph G is the sum of the weights (d(u)d(v)) − 12 of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we first present a sharp lower bound on the Randic ́ index of conjugated unicyclic graphs (unicyclic graphs with perfect matching). Also ..."
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). Also a sharp lower bound on the Randic ́ index of unicyclic graphs is given in terms of the order and given size of matching. KEY WORDS: Randic ́ index, unicyclic graph, given size of matching AMS subject classification: 05C35
The Reciprocal Reverse Wiener Index of Unicyclic Graphs
"... Abstract. The reciprocal reverse Wiener index RΛ(G) of a connected graph G is defined in mathematical chemistry as the sum of weights 1d(G)−dG(u;v) of all unordered pairs of distinct vertices u and vwith dG(u; v) < d(G), where dG(u; v) is the distance between vertices u and v inG and d(G) is the ..."
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(G) is the diameter ofG. We determine the minimum andmaximum reciprocal reverse Wiener indices in the class of nvertex unicyclic graphs and characterize the corresponding extremal graphs. 1.
ON REVERSE DEGREE DISTANCE OF UNICYCLIC GRAPHS
, 2013
"... The reverse degree distance of a connected graph G is defined in discrete mathematical chemistry as rD′(G) = 2(n − 1)md− u∈V (G) dG(u)DG(u), where n, m and d are the number of vertices, the number of edges and the diameter of G, respectively, dG(u) is the degree of vertex u, DG(u) is the sum of di ..."
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of distances between vertex u and all other vertices of G, and V (G) is the vertex set of G. We determine the unicyclic graphs of given girth, number of pendant vertices and maximum degree, respectively, with maximum reverse degree distances. We also determine the unicyclic graphs of given number of vertices
The Wiener index and the Szeged index of benzenoid systems in linear time
 J. Chem. Inf. Comput. Sci
, 1997
"... A linear time algorithm is presented which, for a given benzenoid system G, computes the Wiener index of G. The algorithm is based on an isometric embedding of G into the Cartesian product of three trees, combined with the notion of the Wiener index of vertexweighted graphs. An analogous approach y ..."
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Cited by 30 (7 self)
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A linear time algorithm is presented which, for a given benzenoid system G, computes the Wiener index of G. The algorithm is based on an isometric embedding of G into the Cartesian product of three trees, combined with the notion of the Wiener index of vertexweighted graphs. An analogous approach
Ashrafi, Revised and edge revised Szeged indices of graphs
 ArsMath. Contemporanea
"... The revised Szeged index is a molecular structure descriptor equal to the sum of products [nu(e) + n0(e)/2] × [nv(e) + n0(e)/2] over all edges e = uv of the molecular graph G, where n0(e) is the number of vertices equidistant from u and v, nu(e) is the number of vertices whose distance to vertex u ..."
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The revised Szeged index is a molecular structure descriptor equal to the sum of products [nu(e) + n0(e)/2] × [nv(e) + n0(e)/2] over all edges e = uv of the molecular graph G, where n0(e) is the number of vertices equidistant from u and v, nu(e) is the number of vertices whose distance to vertex u
ON THE WIENER INDEX AND LAPLACIAN COEFFICIENTS OF GRAPHS WITH GIVEN DIAMETER OR RADIUS
, 2011
"... Let G be a simple undirected nvertex graph with the characteristic polynomial of its Laplacian matrix L(G), det(λI − L(G)) = ∑nk=0(−1)kckλn−k. It is well known that for trees the Laplacian coefficient cn−2 is equal to the Wiener index of G. Using a result of Zhou and Gutman on the relation betwee ..."
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Cited by 6 (3 self)
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tion between the Laplacian coefficients and the matching numbers in subdivided bipartite graphs, we characterize first the trees with given diameter and then the connected graphs with given radius which simultaneously minimize all Laplacian coefficients. This approach generalizes recent results of Liu and Pan
Results 1  10
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70