Partial-dual polynomials and signed intersection graphs
نویسندگان
چکیده
Abstract Recently, Gross, Mansour and Tucker introduced the partial-dual polynomial of a ribbon graph as generating function that enumerates all partial duals by Euler genus. It is analogous to extensively studied in topological theory genus embeddings given graph. To investigate polynomial, one only needs focus on bouquets: is, graphs with exactly vertex. In this paper, we shall further show bouquet essentially depends signed intersection rather than itself. That say, two bouquets same have polynomial. We then give characterisation when has planar dual terms its Finally, consider conjecture posed there no orientable whose nonconstant term; false,
منابع مشابه
More Equienergetic Signed Graphs
The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy. In the literature the construction of equienergetic signed graphs are reported. In this paper we obtain the characteristic polynomial and energy of the join of two signed graphs and thereby we give another construction ...
متن کاملTutte Polynomials of Signed Graphs and Jones Polynomials of Some Large Knots
It is well-known that the Jones polynomial of a knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. In this paper, we study the Tutte polynomials for signed graphs. We show that if a signed graph is constructed from a simpler graph via k-thickening or k-stretching, then its Tutte polynomial can be expressed in terms of the Tutte pol...
متن کاملProjective-planar signed graphs and tangled signed graphs
A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained by taking a projective-planar signed graph or a copy of −K5 and then taking 1, 2, and 3-sums with balanced signed graphs.
متن کاملWeak signed Roman domination in graphs
A {em weak signed Roman dominating function} (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as afunction $f:V(G)rightarrow{-1,1,2}$ having the property that $sum_{xin N[v]}f(x)ge 1$ for each $vin V(G)$, where $N[v]$ is theclosed neighborhood of $v$. The weight of a WSRDF is the sum of its function values over all vertices.The weak signed Roman domination number of $G...
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: Forum of Mathematics, Sigma
سال: 2022
ISSN: ['2050-5094']
DOI: https://doi.org/10.1017/fms.2022.62