Extremal subgraphs with respect to vertex degree bounds
نویسندگان
چکیده
منابع مشابه
Vertex-disjoint subgraphs with high degree sums
For a graph G, we denote by σ2(G) the minimum degree sum of two non-adjacent vertices if G is non-complete; otherwise, σ2(G) = +∞. In this paper, we give the following two results; (i) If s1 and s2 are integers with s1, s2 ≥ 2 and if G is a non-complete graph with σ2(G) ≥ 2(s1 + s2 + 1) − 1, then G contains two vertexdisjoint subgraphs H1 and H2 such that each Hi is a graph of order at least si...
متن کاملOn the extremal total irregularity index of n-vertex trees with fixed maximum degree
In the extension of irregularity indices, Abdo et. al. [1] defined the total irregu-larity of a graph G = (V, E) as irrt(G) = 21 Pu,v∈V (G) du − dv, where du denotesthe vertex degree of a vertex u ∈ V (G). In this paper, we investigate the totalirregularity of trees with bounded maximal degree Δ and state integer linear pro-gramming problem which gives standard information about extremal trees a...
متن کاملThe enumeration of vertex induced subgraphs with respect to the number of components
Inspired by the study of community structure in connection networks, we introduce the graph polynomial Q (G;x, y), the bivariate generating function which counts the number of connected components in induced subgraphs. We give a recursive definition of Q (G; x, y) using vertex deletion, vertex contraction and deletion of a vertex together with its neighborhood and prove a universality property....
متن کاملComputing and Sampling Restricted Vertex Degree Subgraphs and Hamiltonian Cycles
Let G = (V, E) be a bipartite graph embedded in a plane (or n-holed torus). Two subgraphs of G differ by a Z-transformation if their symmetric difference consists of the boundary edges of a single face—and if each subgraph contains an alternating set of the edges of that face. For a given φ : V 7→ Z, Sφ is the set of subgraphs of G in which each v ∈ V has degree φ(v). Two elements of Sφ are sai...
متن کاملOn the extremal graphs with respect to bond incident degree indices
Many existing degree based topological indices can be clasified as bond incident degree (BID) indices, whose general form is BID(G) = ∑ uv∈E(G) Ψ(du, dv), where uv is the edge connecting the vertices u, v of the graph G, E(G) is the edge set of G, du is the degree of the vertex u and Ψ is a non-negative real valued (symmetric) function of du and dv. Here, it has been proven that if the extensio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00772-0