Terminal Hosoya Polynomial of Line Graphs

Abstract

The terminal Hosoya polynomial of a graphGis defined asTH(G,λ)=∑k≥1‍dT(G,k)λk, wheredT(G,k)is the number of pairs of pendant vertices ofGthat are at distancek. In this paper we obtain terminal Hosoya polynomial of line graphs.

The sum of hamming distance for some composite graphs relative to vertex-edge incidence matrix

“…As follows that for any vertex (v x ), x = 1, 2, ..., n each expresion deg(v x ) appears (n − 1) times in (2). thus…”

“…There have been many results on Hamming distance and Hamming index produced by adjacency matrix of graph. Ramane and Ganagi [2] discussed Hamming index generated by adjacency matrix of union of graphs and thorn graph. Ganagi and Ramane [3] have established a formula for Hamming distance between two vertices and use this formula to determine Hamming index of some class of graphs such as strongly regular graph, complete graph, complete bipartite graph, cycle and complement of graphs.…”

“…= 2r 1 (s 1 − 2) + 2r 2 (s 2 − 2) + 2r 2 s 1 + 2r 1 s 2 + 2s 2 1 s 2 + 2s 1 s 2 2 − 4s 1 s 2 Given Z 1 is a (s 1 , r 1 ) −graph and Z 2 is a (s 2 , r 2 ) −graph. Given G 1 G 2 be a graph achieved by taking one copy of Z 1 and n copies of Z 2 in such a way that for each i = 1, 2, ..., n, the vertex v i of Z 1 is adjacent to each vertex in the ith copy of Z 2 .…”

“…Given G a graph with vertex set V (Z) = v 1 , v 2 , ..., v n and given C is a (0, 1)-matrix of the graph Z. For any two vertices v x and v y in Z, the Hamming distance of v x and v y ,denoted by Hd(v x , v y ),is defined to be Hd(vx, vy) = Hd(C(x, :), C(y, :)) [2]. The Hamming index generated by a (0, 1)-matrix of a graph Z,indicate by H(Z), is defined to be…”

The Terminal Hosoya Polynomial of Some Families of Composite Graphs

“…and recently Ramane et al studied TH( , ) for the case of line graphs [13]. As we can expect, the terminal Wiener index, denoted by TW( ), is obtained from TH( , ) as…”