Extremal (n, m)-Graphs with Respect to Distance-Degree-Based Topological Indices

作者：Xu Kexiang^*; Klavzar Sandi; Das Kinkar Ch; Wang Jinlan

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2014, 72(3): 865-880.

In chemical graph theory, distance-degree-based topological indices are expressions of the form Sigma(u not equal v) F(deg(u), deg(v), d(u, v)), where F is a function, deg(u) the degree of u, and d(u, v) the distance between u and v. Setting F to be (deg(u) + deg(v))d(u, v), deg(u)deg(v)d(u, v), (deg(u) + deg(v))d(u,v)(-1), and deg(u)deg(v)d(u, v)(-1), we get the degree distance index DD, the Gutman index Gut, the additively weighted Harary index H-A, and the multiplicatively weighted Harary index H-M, respectively. %26lt;br%26gt;Let g(n,m) be the set of connected graphs of order n and size m. It is proved that if G is an element of g(n,m) where 4 %26lt;= n %26lt;= m %26lt;= 2n - 4, then H-A(G) %26lt;= (m(m + 5) + 2(n - 1)(n - 3))/2 and DD (G) %26gt;= (4m -n)(n -1) - (m-n+1)(m -n+ 6). The extremal graphs are characterized in both cases and are the same. Similarly, the graphs from g(n,m) with m = n + (k 2) - k, 2 %26lt;= k %26lt;= n - 1, maximizing the multiplicatively weighted Harary index and minimizing the Gutman index are obtained.

• 出版日期2014
• 单位南京大学