[PDF] Top 20 Resistance Distance and Kirchhoff Index of Graphs with Pockets

... matrix X such that MXM = M, XMX = X and MX = XM. It is known that M # exists if and only if rank ( M ) = rank ( M 2 ) ([17],[18]). If M is real symmetric, then M # exists and M # is a symmetric { 1 } -inverse of M. ... See full document

... factor graphs. Then the resistance distance and Kirchhoff index of these graphs can be derived from the resistance distance and Kirchhoff index of the ... See full document

... the resistance distance between two arbitrary vertices in an electrical network can be obtained in terms of the eigenvalues and eigenvectors of the combinato- rial Laplacian matrix and the normalized ... See full document

... effective resistance between them when unit resistors are placed on every edge of ...The Kirchhoff index Kf (G) is the sum of resistance distances between all pairs of vertices of ...the ... See full document

... the resistance distance between these vertices are denoted by r ij ...new distance is an effective resistance between nodes v i and v j according to Ohm's law ...all resistance ... See full document

... In the past decade, interest in graph energy has increased and similar definitions have been formulated for other matrices associated with a graph, such as the Laplacian, normalized Laplacian, distance matrices, ... See full document

... 9. S. Huang, J. Zhou and C. Bu, Some results on Kirchhoff index and degree– Kirchhoff index, MATCH Commun. Math. Comput. Chem. 75 (2016) 207–222. 10. D. J. Klein and M. Randi'c, ... See full document

... topological index along the line of this strategy was developed by Klein and Randić, who defined the so-called Kirchhoff index, Kf ...The Kirchhoff index is defined in an analogous way ... See full document

... effective resistance and param- eters related to vertex hitting times of random walks on G(n, ...effective resistance R(i, j) between two vertices i, j of G(n, p) and show that with high probability for a ... See full document

... In this paper, based on the results in ref. [15], we study the relation between Wiener number W , hyper-Wiener number R , Wiener vector WV , hyper- Wiener vector HWV , Hosoya polynomial H , hyper-Hosoya polynomial HH and ... See full document

... as the smallest µ-length of P. In a fuzzy graph G : (V,σ ,µ), dµ(u, v) is a metric on V ∀ u,v ∈ V . The strength of connectedness between two nodes u and v is defined as the maximum of the strengths of all paths between ... See full document

... cyclotomic index of G is defined as  p ( )(mod ) q p and is denoted by ...cyclotomic index of some special type of ...cyclotomic index of certain ... See full document

... Randić index, first general Zagreb index, geometric arithmetic index, atom-bond connectivity index and general sum-connectivity index of the total graph of the tadpole graphs, ... See full document

... A regular graph is a graph where each vertex has the same number of neighbors. A regular graph with vertices of degree k is called a k-regular graph or regular graph of degree k. In this section, we study the conditions ... See full document

... By lemma 2.1, G has exactly two pendent vertices and degree of the remaining n − 2 vertices is greater than or equal to 2. Therefore, dm(G) = n or n − 1. Definition 2.2. Mycielski construction to create triangle-free ... See full document

... topological index based on degrees and inverse of distances between all pairs of ...degree distance as RDD(G) =  { , } u v  V G ( ) ( ( ) d u  d v ( ))[ ( , )] d u v  1 , where the d(u,v) denotes the ... See full document

... the graphs S(G), R(G), Q(G), and T(G), and they also computed the Wiener index of these graph operations in terms of W(F(G)) and W(H), where F is one of the symbols S, R, Q, ...sum-connectivity index ... See full document

... 3. Distance-Balanced Graphs with Maximum Degree n − 2 In this section, we prove that any distance-balanced graph G with ∆(G) = n − 2 is a regular graph using this, we construct a ... See full document

... a vertex v in G. The number of elements in the vertex set of a graph G is called the order of G and is denoted by v (G). The number of elements in the edge set of a graph G is called the size of G and is denoted by e(G). ... See full document

... of distance closed set is defined and studied in the doctoral thesis of Janakiraman [5] and the concept of distance closed sets in graph theory is due to the related concept of ideals in ring theory in ... See full document