The Detour Polynomials and Detour Index of an m-Ring of 2n-Cycles, m,n ≥ 2
نویسندگان
چکیده
منابع مشابه
On edge detour index polynomials
The edge detour index polynomials were recently introduced for computing the edge detour indices. In this paper we find relations among edge detour polynomials for the 2-dimensional graph of $TUC_4C_8(S)$ in a Euclidean plane and $TUC4C8(S)$ nanotorus.
متن کاملon edge detour index polynomials
the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.
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The detour index of a connected graph is defined as the sum of the detour distances (lengths of longest paths) between unordered pairs of vertices of the graph. We give bounds for the detour index, determine the graphs with minimum and maximum detour indices respectively in the class of n-vertex unicyclic graphs with cycle length r, where 3 ≤ r ≤ n−2, and the graphs with the first, the second a...
متن کاملThe explicit relation among the edge versions of detour index
The vertex version of detour index was defined during the works on connected graph in chemistry. The edge versions of detour index have been introduced ecently. In this paper, the explicit relations among edge versions of detour index have been declared and due to these relations, we compute the edge detour indices for some well-known graphs.
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A spanning subgraph H of a graph G is a 2-detour subgraph of G if for each x, y ∈ V (G), dH(x, y) ≤ dG(x, y) + 2. We prove a conjecture of Erdős, Hamburger, Pippert, and Weakley by showing that for some positive constant c and every n, each 2-detour subgraph of the n-dimensional hypercube Qn has at least c log2 n · 2n edges.
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ژورنال
عنوان ژورنال: Mathematical Sciences Letters
سال: 2014
ISSN: 2090-9616,2090-9624
DOI: 10.12785/msl/030205