Let G be a simple connected graph of order at least 2. An i-subset of V (G) is a subset of V
(G) of cardinality i. An i-clique is an i-subset which induces a complete subgraph of G. The …

The eccentric connectivity polynomial (ECP) of a connected graph G=(V (G), E (G)) is
described as ξ c G, y=∑ a∈ VG deg G ayec G a, where ecG (a) and degG (a) represent the …

Zero forcing is an iterative graph coloring process, where given a set of initially colored
vertices, a colored vertex with a single uncolored neighbor causes that neighbor to become …

We use Wagner's weighted subgraph counting polynomial to prove that the partition function
of the anti-ferromagnetic Ising model on line graphs is real rooted and to prove that roots of …

The Laplacian matrix, sometimes also called the admittance matrix (Cvetković et al. 1998,
Babić et al. 2002) or Kirchhoff matrix, of a graph G, where G=(V, E) is an undirected …

A placement of chess pieces on a chessboard is called dominating, if each free square of
the chessboard is under attack by at least one piece. In this contribution we compute the …

Roots of graph polynomials such as the characteristic polynomial, the chromatic polynomial,
the matching polynomial, and many others are widely studied. In this paper we examine to …

In this article, we study problems where one has to prove that certain graph parameter
attains its maximum at the star and its minimum at the path among the trees on a fixed …

Let G be a simple graph of order n and size m. An edge covering of the graph G is a set of
edges such that every vertex of the graph is incident to at least one edge of the set. Let e (G …

Convex Subgraph Polynomials of the Join and the Composition of Graphs Page 1 International
Journal of Mathematical Analysis Vol. 10, 2016, no. 11, 515 - 529 HIKARI Ltd, www.m-hikari.com …