Results 181 to 190 of about 7,067 (209)
Some of the next articles are maybe not open access.
Bipartite graphs as polynomials and polynomials as bipartite graphs
Journal of Algebra and Its Applications, 2020The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial [Formula: see text], and any directed finite bipartite graph can be considered as a polynomial [Formula: see text], and vise verse. We also show that the multiplication in the semirings [Formula: see text], [Formula: see text] corresponds to an
Grinblat, Andrey, Lopatkin, Viktor
openaire +2 more sources
The American Mathematical Monthly, 1963
(1963). On the Polynomial of a Graph. The American Mathematical Monthly: Vol. 70, No. 1, pp. 30-36.
openaire +1 more source
(1963). On the Polynomial of a Graph. The American Mathematical Monthly: Vol. 70, No. 1, pp. 30-36.
openaire +1 more source
SIAM Journal on Algebraic Discrete Methods, 1983
For a graph G, let $A( G )$ be its adjacency matrix. Let $\varphi _G ( x )$ be the characteristic polynomial of G. Let J be a matrix with all entries equal to 1. Let $\psi _G ( x ) = \varphi_{A ( G ) - J} ( x ) - \varphi_G ( x )$. In this paper, we show that the haracteristic polynomials of the join $G + H$, the complement $\bar G$ and the composition $
openaire +1 more source
For a graph G, let $A( G )$ be its adjacency matrix. Let $\varphi _G ( x )$ be the characteristic polynomial of G. Let J be a matrix with all entries equal to 1. Let $\psi _G ( x ) = \varphi_{A ( G ) - J} ( x ) - \varphi_G ( x )$. In this paper, we show that the haracteristic polynomials of the join $G + H$, the complement $\bar G$ and the composition $
openaire +1 more source
Mathematics of the USSR-Sbornik, 1985
Translation from Mat. Sb., Nov. Ser. 123(165), No.3, 407-421 (Russian) (1984; Zbl 0548.05033).
openaire +3 more sources
Translation from Mat. Sb., Nov. Ser. 123(165), No.3, 407-421 (Russian) (1984; Zbl 0548.05033).
openaire +3 more sources
Journal of Graph Theory, 2002
AbstractThe tension polynomial FG(k) of a graph G, evaluating the number of nowhere‐zero ℤk‐tensions in G, is the nontrivial divisor of the chromatic polynomial χG(k) of G, in that χG(k) = kc(G)FG(k), where c(G) denotes the number of components of G. We introduce the integral tension polynomial IG(k), which evaluates the number of nowhere‐zero integral
openaire +2 more sources
AbstractThe tension polynomial FG(k) of a graph G, evaluating the number of nowhere‐zero ℤk‐tensions in G, is the nontrivial divisor of the chromatic polynomial χG(k) of G, in that χG(k) = kc(G)FG(k), where c(G) denotes the number of components of G. We introduce the integral tension polynomial IG(k), which evaluates the number of nowhere‐zero integral
openaire +2 more sources
Graphs with polynomial growth are covering graphs
Graphs and Combinatorics, 1992Let \(X(V,E)\) be a simple undirected locally finite graph with vertex set \(V(X)\) and edge set \(E(X)\). The growth function of \(X\), with respect to a vertex \(v\in V(X)\) is defined by \(f_ X(v,0)=1\) and \(f_ X(v,n)=|\{w\in V(X)| d(v,w)\leq n\}|\), \(n\in N\), where \(d(v,w)\) denotes the distance between \(v\) and \(w\).
Chris D. Godsil, Norbert Seifter
openaire +1 more source
Neighborhood and Domination Polynomials of Graphs
Graphs and Combinatorics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Irene Heinrich, Peter Tittmann 0001
openaire +1 more source
Polynomial invariants of graphs II
Graphs and Combinatorics, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seiya Negami, Katsuhiro Ota
openaire +2 more sources
The lattice polynomial of a graph.
Ars Comb., 2000The authors associate with a finite simple graph \(G\) the polynomial (which they call lattice polynomial) \(\pi (G,t)=\sum \mu (H)t^{| H| }\) where the summation goes over the poset \(P\) of connected induced subgraphs of \(G\) (ordered by inclusion), \(\mu \) is the Möbius function of \(P\), and \(| H| \) is the number of vertices in \(H\).
Jonathan Wiens, Kara L. Nance
openaire +1 more source
On connectivity polynomial of graphs
Discrete Mathematics, Algorithms and ApplicationsIn this paper we introduce a new graph polynomial, say connectivity polynomial. Let [Formula: see text] be a simple graph of order [Formula: see text]. The connectivity polynomial of [Formula: see text], denoted by [Formula: see text], is [Formula: see text], where [Formula: see text] and [Formula: see text] (for [Formula: see text]) is the number of ...
openaire +1 more source